id sid tid token lemma pos ajst-27745 1 1 academic academic ADJ ajst-27745 1 2 journal journal NOUN ajst-27745 1 3 of of ADP ajst-27745 1 4 science science NOUN ajst-27745 1 5 and and CCONJ ajst-27745 1 6 technology technology NOUN ajst-27745 1 7 issn issn NOUN ajst-27745 1 8 : : PUNCT ajst-27745 1 9 2771 2771 NUM ajst-27745 1 10 - - SYM ajst-27745 1 11 3032 3032 NUM ajst-27745 1 12 | | NOUN ajst-27745 1 13 vol vol NOUN ajst-27745 1 14 . . PROPN ajst-27745 1 15 13 13 NUM ajst-27745 1 16 , , PUNCT ajst-27745 1 17 no no INTJ ajst-27745 1 18 . . NOUN ajst-27745 1 19 2 2 NUM ajst-27745 1 20 , , PUNCT ajst-27745 1 21 2024 2024 NUM ajst-27745 1 22 297 297 NUM ajst-27745 1 23 motion motion NOUN ajst-27745 1 24 path path NOUN ajst-27745 1 25 study study NOUN ajst-27745 1 26 based base VERB ajst-27745 1 27 on on ADP ajst-27745 1 28 isometric isometric ADJ ajst-27745 1 29 solenoids solenoid NOUN ajst-27745 1 30 and and CCONJ ajst-27745 1 31 discrete discrete ADJ ajst-27745 1 32 simulation simulation NOUN ajst-27745 1 33 chenhui chenhui PROPN ajst-27745 1 34 wang1 wang1 PROPN ajst-27745 1 35 , , PUNCT ajst-27745 1 36 * * PUNCT ajst-27745 2 1 1school 1school NUM ajst-27745 2 2 of of ADP ajst-27745 2 3 meteorology meteorology NOUN ajst-27745 2 4 and and CCONJ ajst-27745 2 5 oceanography oceanography NOUN ajst-27745 2 6 , , PUNCT ajst-27745 2 7 national national ADJ ajst-27745 2 8 university university PROPN ajst-27745 2 9 of of ADP ajst-27745 2 10 defense defense PROPN ajst-27745 2 11 technology technology PROPN ajst-27745 2 12 , , PUNCT ajst-27745 2 13 changsha changsha PROPN ajst-27745 2 14 , , PUNCT ajst-27745 2 15 china china PROPN ajst-27745 2 16 * * PUNCT ajst-27745 2 17 corresponding correspond VERB ajst-27745 2 18 author author NOUN ajst-27745 2 19 : : PUNCT ajst-27745 2 20 1992029712@qq.com 1992029712@qq.com NUM ajst-27745 2 21 abstract abstract NOUN ajst-27745 2 22 : : PUNCT ajst-27745 2 23 this this DET ajst-27745 2 24 paper paper NOUN ajst-27745 2 25 focuses focus VERB ajst-27745 2 26 on on ADP ajst-27745 2 27 the the DET ajst-27745 2 28 position position NOUN ajst-27745 2 29 , , PUNCT ajst-27745 2 30 speed speed NOUN ajst-27745 2 31 change change NOUN ajst-27745 2 32 and and CCONJ ajst-27745 2 33 collision collision NOUN ajst-27745 2 34 detection detection NOUN ajst-27745 2 35 problems problem NOUN ajst-27745 2 36 during during ADP ajst-27745 2 37 the the DET ajst-27745 2 38 traveling travel VERB ajst-27745 2 39 process process NOUN ajst-27745 2 40 of of ADP ajst-27745 2 41 the the DET ajst-27745 2 42 bench bench NOUN ajst-27745 2 43 dragon dragon NOUN ajst-27745 2 44 from from ADP ajst-27745 2 45 both both CCONJ ajst-27745 2 46 physical physical ADJ ajst-27745 2 47 and and CCONJ ajst-27745 2 48 mathematical mathematical ADJ ajst-27745 2 49 perspectives perspective NOUN ajst-27745 2 50 . . PUNCT ajst-27745 3 1 firstly firstly ADV ajst-27745 3 2 , , PUNCT ajst-27745 3 3 based base VERB ajst-27745 3 4 on on ADP ajst-27745 3 5 the the DET ajst-27745 3 6 equidistance equidistance NOUN ajst-27745 3 7 solenoid solenoid NOUN ajst-27745 3 8 equation equation NOUN ajst-27745 3 9 and and CCONJ ajst-27745 3 10 the the DET ajst-27745 3 11 mechanical mechanical ADJ ajst-27745 3 12 arm arm NOUN ajst-27745 3 13 model model NOUN ajst-27745 3 14 , , PUNCT ajst-27745 3 15 this this DET ajst-27745 3 16 paper paper NOUN ajst-27745 3 17 iteratively iteratively ADV ajst-27745 3 18 recursively recursively ADV ajst-27745 3 19 starts start VERB ajst-27745 3 20 from from ADP ajst-27745 3 21 the the DET ajst-27745 3 22 dragon dragon NOUN ajst-27745 3 23 head head NOUN ajst-27745 3 24 and and CCONJ ajst-27745 3 25 sequentially sequentially ADV ajst-27745 3 26 solves solve VERB ajst-27745 3 27 the the DET ajst-27745 3 28 position position NOUN ajst-27745 3 29 of of ADP ajst-27745 3 30 each each DET ajst-27745 3 31 section section NOUN ajst-27745 3 32 of of ADP ajst-27745 3 33 the the DET ajst-27745 3 34 bench bench NOUN ajst-27745 3 35 in in ADP ajst-27745 3 36 the the DET ajst-27745 3 37 traveling travel VERB ajst-27745 3 38 process process NOUN ajst-27745 3 39 . . PUNCT ajst-27745 4 1 secondly secondly ADV ajst-27745 4 2 , , PUNCT ajst-27745 4 3 this this DET ajst-27745 4 4 paper paper NOUN ajst-27745 4 5 combines combine VERB ajst-27745 4 6 the the DET ajst-27745 4 7 velocity velocity NOUN ajst-27745 4 8 analysis analysis NOUN ajst-27745 4 9 of of ADP ajst-27745 4 10 the the DET ajst-27745 4 11 rigid rigid ADJ ajst-27745 4 12 rod rod NOUN ajst-27745 4 13 and and CCONJ ajst-27745 4 14 the the DET ajst-27745 4 15 nature nature NOUN ajst-27745 4 16 of of ADP ajst-27745 4 17 isometric isometric ADJ ajst-27745 4 18 solenoid solenoid NOUN ajst-27745 4 19 , , PUNCT ajst-27745 4 20 and and CCONJ ajst-27745 4 21 also also ADV ajst-27745 4 22 solves solve VERB ajst-27745 4 23 the the DET ajst-27745 4 24 position position NOUN ajst-27745 4 25 of of ADP ajst-27745 4 26 each each DET ajst-27745 4 27 section section NOUN ajst-27745 4 28 of of ADP ajst-27745 4 29 the the DET ajst-27745 4 30 bench bench NOUN ajst-27745 4 31 in in ADP ajst-27745 4 32 the the DET ajst-27745 4 33 traveling travel VERB ajst-27745 4 34 process process NOUN ajst-27745 4 35 sequentially sequentially ADV ajst-27745 4 36 in in ADP ajst-27745 4 37 the the DET ajst-27745 4 38 form form NOUN ajst-27745 4 39 of of ADP ajst-27745 4 40 iterative iterative ADJ ajst-27745 4 41 recursion recursion NOUN ajst-27745 4 42 . . PUNCT ajst-27745 5 1 finally finally ADV ajst-27745 5 2 , , PUNCT ajst-27745 5 3 this this DET ajst-27745 5 4 paper paper NOUN ajst-27745 5 5 discretizes discretize VERB ajst-27745 5 6 the the DET ajst-27745 5 7 disk disk NOUN ajst-27745 5 8 - - PUNCT ajst-27745 5 9 in in ADP ajst-27745 5 10 trajectory trajectory NOUN ajst-27745 5 11 and and CCONJ ajst-27745 5 12 carries carry VERB ajst-27745 5 13 out out ADP ajst-27745 5 14 collision collision NOUN ajst-27745 5 15 detection detection NOUN ajst-27745 5 16 , , PUNCT ajst-27745 5 17 so so SCONJ ajst-27745 5 18 as as SCONJ ajst-27745 5 19 to to PART ajst-27745 5 20 obtain obtain VERB ajst-27745 5 21 the the DET ajst-27745 5 22 time time NOUN ajst-27745 5 23 , , PUNCT ajst-27745 5 24 position position NOUN ajst-27745 5 25 , , PUNCT ajst-27745 5 26 velocity velocity NOUN ajst-27745 5 27 and and CCONJ ajst-27745 5 28 other other ADJ ajst-27745 5 29 information information NOUN ajst-27745 5 30 at at ADP ajst-27745 5 31 the the DET ajst-27745 5 32 termination termination NOUN ajst-27745 5 33 moment moment NOUN ajst-27745 5 34 . . PUNCT ajst-27745 6 1 the the DET ajst-27745 6 2 study study NOUN ajst-27745 6 3 shows show VERB ajst-27745 6 4 that that SCONJ ajst-27745 6 5 the the DET ajst-27745 6 6 model model NOUN ajst-27745 6 7 can can AUX ajst-27745 6 8 effectively effectively ADV ajst-27745 6 9 solve solve VERB ajst-27745 6 10 the the DET ajst-27745 6 11 complex complex ADJ ajst-27745 6 12 optimization optimization NOUN ajst-27745 6 13 problem problem NOUN ajst-27745 6 14 in in ADP ajst-27745 6 15 the the DET ajst-27745 6 16 marching marching NOUN ajst-27745 6 17 process process NOUN ajst-27745 6 18 of of ADP ajst-27745 6 19 the the DET ajst-27745 6 20 dragon dragon NOUN ajst-27745 6 21 dance dance NOUN ajst-27745 6 22 team team NOUN ajst-27745 6 23 . . PUNCT ajst-27745 7 1 keywords keyword NOUN ajst-27745 7 2 : : PUNCT ajst-27745 7 3 isometric isometric ADJ ajst-27745 7 4 solenoids solenoid NOUN ajst-27745 7 5 , , PUNCT ajst-27745 7 6 iterative iterative NOUN ajst-27745 7 7 recursion recursion NOUN ajst-27745 7 8 , , PUNCT ajst-27745 7 9 rigid rigid ADJ ajst-27745 7 10 body body NOUN ajst-27745 7 11 rods rod NOUN ajst-27745 7 12 , , PUNCT ajst-27745 7 13 discrete discrete ADJ ajst-27745 7 14 simulation simulation NOUN ajst-27745 7 15 . . PUNCT ajst-27745 8 1 1 1 X ajst-27745 8 2 . . X ajst-27745 8 3 introduction introduction NOUN ajst-27745 8 4 the the DET ajst-27745 8 5 purpose purpose NOUN ajst-27745 8 6 of of ADP ajst-27745 8 7 this this DET ajst-27745 8 8 paper paper NOUN ajst-27745 8 9 is be AUX ajst-27745 8 10 to to PART ajst-27745 8 11 study study VERB ajst-27745 8 12 in in ADP ajst-27745 8 13 depth depth NOUN ajst-27745 8 14 the the DET ajst-27745 8 15 dynamics dynamic NOUN ajst-27745 8 16 of of ADP ajst-27745 8 17 the the DET ajst-27745 8 18 bench bench NOUN ajst-27745 8 19 dragon dragon NOUN ajst-27745 8 20 during during ADP ajst-27745 8 21 its its PRON ajst-27745 8 22 traveling travel VERB ajst-27745 8 23 process process NOUN ajst-27745 8 24 from from ADP ajst-27745 8 25 the the DET ajst-27745 8 26 physical physical ADJ ajst-27745 8 27 and and CCONJ ajst-27745 8 28 mathematical mathematical ADJ ajst-27745 8 29 perspectives perspective NOUN ajst-27745 8 30 , , PUNCT ajst-27745 8 31 so so SCONJ ajst-27745 8 32 as as SCONJ ajst-27745 8 33 to to PART ajst-27745 8 34 analyze analyze VERB ajst-27745 8 35 the the DET ajst-27745 8 36 key key ADJ ajst-27745 8 37 factors factor NOUN ajst-27745 8 38 such such ADJ ajst-27745 8 39 as as ADP ajst-27745 8 40 the the DET ajst-27745 8 41 position position NOUN ajst-27745 8 42 , , PUNCT ajst-27745 8 43 velocity velocity NOUN ajst-27745 8 44 change change NOUN ajst-27745 8 45 and and CCONJ ajst-27745 8 46 collision collision NOUN ajst-27745 8 47 detection detection NOUN ajst-27745 8 48 during during ADP ajst-27745 8 49 the the DET ajst-27745 8 50 traveling travel VERB ajst-27745 8 51 process process NOUN ajst-27745 8 52 of of ADP ajst-27745 8 53 the the DET ajst-27745 8 54 bench bench NOUN ajst-27745 8 55 dragon dragon NOUN ajst-27745 9 1 [ [ X ajst-27745 9 2 1,2,3 1,2,3 NUM ajst-27745 9 3 ] ] PUNCT ajst-27745 9 4 . . PUNCT ajst-27745 10 1 in in ADP ajst-27745 10 2 this this DET ajst-27745 10 3 paper paper NOUN ajst-27745 10 4 , , PUNCT ajst-27745 10 5 firstly firstly ADV ajst-27745 10 6 , , PUNCT ajst-27745 10 7 based base VERB ajst-27745 10 8 on on ADP ajst-27745 10 9 the the DET ajst-27745 10 10 equidistant equidistant ADJ ajst-27745 10 11 solenoidal solenoidal ADJ ajst-27745 10 12 equation equation NOUN ajst-27745 10 13 and and CCONJ ajst-27745 10 14 robotic robotic ADJ ajst-27745 10 15 arm arm NOUN ajst-27745 10 16 model model NOUN ajst-27745 10 17 , , PUNCT ajst-27745 10 18 the the DET ajst-27745 10 19 position position NOUN ajst-27745 10 20 of of ADP ajst-27745 10 21 each each DET ajst-27745 10 22 section section NOUN ajst-27745 10 23 of of ADP ajst-27745 10 24 the the DET ajst-27745 10 25 bench bench NOUN ajst-27745 10 26 during during ADP ajst-27745 10 27 the the DET ajst-27745 10 28 traveling travel VERB ajst-27745 10 29 process process NOUN ajst-27745 10 30 is be AUX ajst-27745 10 31 solved solve VERB ajst-27745 10 32 by by ADP ajst-27745 10 33 iterative iterative ADJ ajst-27745 10 34 recursive recursive ADJ ajst-27745 10 35 method method NOUN ajst-27745 10 36 [ [ X ajst-27745 10 37 4,5 4,5 NUM ajst-27745 10 38 ] ] PUNCT ajst-27745 10 39 . . PUNCT ajst-27745 11 1 secondly secondly ADV ajst-27745 11 2 , , PUNCT ajst-27745 11 3 this this DET ajst-27745 11 4 paper paper NOUN ajst-27745 11 5 combines combine VERB ajst-27745 11 6 the the DET ajst-27745 11 7 velocity velocity NOUN ajst-27745 11 8 analysis analysis NOUN ajst-27745 11 9 of of ADP ajst-27745 11 10 rigid rigid ADJ ajst-27745 11 11 - - PUNCT ajst-27745 11 12 body body NOUN ajst-27745 11 13 rod rod NOUN ajst-27745 11 14 and and CCONJ ajst-27745 11 15 the the DET ajst-27745 11 16 nature nature NOUN ajst-27745 11 17 of of ADP ajst-27745 11 18 isometric isometric ADJ ajst-27745 11 19 solenoid solenoid NOUN ajst-27745 11 20 to to PART ajst-27745 11 21 further far ADV ajst-27745 11 22 solve solve VERB ajst-27745 11 23 the the DET ajst-27745 11 24 position position NOUN ajst-27745 11 25 of of ADP ajst-27745 11 26 each each DET ajst-27745 11 27 section section NOUN ajst-27745 11 28 of of ADP ajst-27745 11 29 the the DET ajst-27745 11 30 bench bench NOUN ajst-27745 11 31 during during ADP ajst-27745 11 32 the the DET ajst-27745 11 33 traveling travel VERB ajst-27745 11 34 process process NOUN ajst-27745 11 35 . . PUNCT ajst-27745 12 1 the the DET ajst-27745 12 2 introduction introduction NOUN ajst-27745 12 3 of of ADP ajst-27745 12 4 the the DET ajst-27745 12 5 rigid rigid ADJ ajst-27745 12 6 - - PUNCT ajst-27745 12 7 body body NOUN ajst-27745 12 8 rod rod NOUN ajst-27745 12 9 model model NOUN ajst-27745 12 10 allows allow VERB ajst-27745 12 11 us we PRON ajst-27745 12 12 to to PART ajst-27745 12 13 analyze analyze VERB ajst-27745 12 14 the the DET ajst-27745 12 15 dynamic dynamic ADJ ajst-27745 12 16 characteristics characteristic NOUN ajst-27745 12 17 of of ADP ajst-27745 12 18 the the DET ajst-27745 12 19 bench bench NOUN ajst-27745 12 20 dragon dragon NOUN ajst-27745 12 21 during during ADP ajst-27745 12 22 the the DET ajst-27745 12 23 traveling travel VERB ajst-27745 12 24 process process NOUN ajst-27745 12 25 more more ADV ajst-27745 12 26 accurately accurately ADV ajst-27745 12 27 , , PUNCT ajst-27745 12 28 including include VERB ajst-27745 12 29 the the DET ajst-27745 12 30 changes change NOUN ajst-27745 12 31 of of ADP ajst-27745 12 32 velocity velocity NOUN ajst-27745 12 33 and and CCONJ ajst-27745 12 34 acceleration acceleration NOUN ajst-27745 13 1 [ [ X ajst-27745 13 2 6,7 6,7 NUM ajst-27745 13 3 ] ] PUNCT ajst-27745 13 4 . . PUNCT ajst-27745 14 1 finally finally ADV ajst-27745 14 2 , , PUNCT ajst-27745 14 3 in in ADP ajst-27745 14 4 this this DET ajst-27745 14 5 paper paper NOUN ajst-27745 14 6 , , PUNCT ajst-27745 14 7 the the DET ajst-27745 14 8 diskin diskin NOUN ajst-27745 14 9 trajectory trajectory NOUN ajst-27745 14 10 is be AUX ajst-27745 14 11 discretized discretize VERB ajst-27745 14 12 and and CCONJ ajst-27745 14 13 collision collision NOUN ajst-27745 14 14 detection detection NOUN ajst-27745 14 15 is be AUX ajst-27745 14 16 carried carry VERB ajst-27745 14 17 out out ADP ajst-27745 14 18 to to PART ajst-27745 14 19 obtain obtain VERB ajst-27745 14 20 the the DET ajst-27745 14 21 key key ADJ ajst-27745 14 22 information information NOUN ajst-27745 14 23 such such ADJ ajst-27745 14 24 as as ADP ajst-27745 14 25 time time NOUN ajst-27745 14 26 , , PUNCT ajst-27745 14 27 position position NOUN ajst-27745 14 28 and and CCONJ ajst-27745 14 29 velocity velocity NOUN ajst-27745 14 30 at at ADP ajst-27745 14 31 the the DET ajst-27745 14 32 termination termination NOUN ajst-27745 14 33 moment moment NOUN ajst-27745 14 34 . . PUNCT ajst-27745 15 1 through through ADP ajst-27745 15 2 the the DET ajst-27745 15 3 discrete discrete ADJ ajst-27745 15 4 simulation simulation NOUN ajst-27745 15 5 technique technique NOUN ajst-27745 15 6 , , PUNCT ajst-27745 15 7 we we PRON ajst-27745 15 8 can can AUX ajst-27745 15 9 simulate simulate VERB ajst-27745 15 10 various various ADJ ajst-27745 15 11 situations situation NOUN ajst-27745 15 12 that that PRON ajst-27745 15 13 may may AUX ajst-27745 15 14 be be AUX ajst-27745 15 15 encountered encounter VERB ajst-27745 15 16 by by ADP ajst-27745 15 17 the the DET ajst-27745 15 18 bench bench NOUN ajst-27745 15 19 dragon dragon NOUN ajst-27745 15 20 in in ADP ajst-27745 15 21 the the DET ajst-27745 15 22 actual actual ADJ ajst-27745 15 23 traveling travel VERB ajst-27745 15 24 process process NOUN ajst-27745 15 25 , , PUNCT ajst-27745 15 26 so so SCONJ ajst-27745 15 27 as as SCONJ ajst-27745 15 28 to to PART ajst-27745 15 29 optimize optimize VERB ajst-27745 15 30 the the DET ajst-27745 15 31 performance performance NOUN ajst-27745 15 32 scheme scheme NOUN ajst-27745 15 33 and and CCONJ ajst-27745 15 34 avoid avoid VERB ajst-27745 15 35 the the DET ajst-27745 15 36 occurrence occurrence NOUN ajst-27745 15 37 of of ADP ajst-27745 15 38 collision collision NOUN ajst-27745 15 39 and and CCONJ ajst-27745 15 40 other other ADJ ajst-27745 15 41 unforeseen unforeseen ADJ ajst-27745 15 42 situations situation NOUN ajst-27745 15 43 [ [ X ajst-27745 15 44 8,9 8,9 NUM ajst-27745 15 45 ] ] PUNCT ajst-27745 15 46 . . PUNCT ajst-27745 16 1 2 2 X ajst-27745 16 2 . . X ajst-27745 16 3 modeling modeling NOUN ajst-27745 16 4 of of ADP ajst-27745 16 5 bench bench NOUN ajst-27745 16 6 dragon dragon NOUN ajst-27745 16 7 travel travel NOUN ajst-27745 16 8 process process NOUN ajst-27745 16 9 based base VERB ajst-27745 16 10 on on ADP ajst-27745 16 11 isometric isometric ADJ ajst-27745 16 12 solenoidal solenoidal ADJ ajst-27745 16 13 equation equation NOUN ajst-27745 16 14 and and CCONJ ajst-27745 16 15 recursive recursive ADJ ajst-27745 16 16 method method NOUN ajst-27745 16 17 through through ADP ajst-27745 16 18 field field NOUN ajst-27745 16 19 research research NOUN ajst-27745 16 20 , , PUNCT ajst-27745 16 21 we we PRON ajst-27745 16 22 collected collect VERB ajst-27745 16 23 data datum NOUN ajst-27745 16 24 on on ADP ajst-27745 16 25 a a DET ajst-27745 16 26 bench bench NOUN ajst-27745 16 27 dragon dragon NOUN ajst-27745 16 28 , , PUNCT ajst-27745 16 29 which which PRON ajst-27745 16 30 consists consist VERB ajst-27745 16 31 of of ADP ajst-27745 16 32 223 223 NUM ajst-27745 16 33 sections section NOUN ajst-27745 16 34 of of ADP ajst-27745 16 35 benches bench NOUN ajst-27745 16 36 , , PUNCT ajst-27745 16 37 of of ADP ajst-27745 16 38 which which PRON ajst-27745 16 39 the the DET ajst-27745 16 40 first first ADJ ajst-27745 16 41 section section NOUN ajst-27745 16 42 is be AUX ajst-27745 16 43 the the DET ajst-27745 16 44 dragon dragon NOUN ajst-27745 16 45 's 's PART ajst-27745 16 46 head head NOUN ajst-27745 16 47 , , PUNCT ajst-27745 16 48 the the DET ajst-27745 16 49 next next ADJ ajst-27745 16 50 221 221 NUM ajst-27745 16 51 sections section NOUN ajst-27745 16 52 are be AUX ajst-27745 16 53 the the DET ajst-27745 16 54 dragon dragon NOUN ajst-27745 16 55 's 's PART ajst-27745 16 56 body body NOUN ajst-27745 16 57 , , PUNCT ajst-27745 16 58 and and CCONJ ajst-27745 16 59 the the DET ajst-27745 16 60 last last ADJ ajst-27745 16 61 section section NOUN ajst-27745 16 62 is be AUX ajst-27745 16 63 the the DET ajst-27745 16 64 dragon dragon NOUN ajst-27745 16 65 's 's PART ajst-27745 16 66 tail tail NOUN ajst-27745 16 67 . . PUNCT ajst-27745 17 1 the the DET ajst-27745 17 2 length length NOUN ajst-27745 17 3 of of ADP ajst-27745 17 4 the the DET ajst-27745 17 5 dragon dragon NOUN ajst-27745 17 6 's 's PART ajst-27745 17 7 head head NOUN ajst-27745 17 8 is be AUX ajst-27745 17 9 341 341 NUM ajst-27745 17 10 cm cm NOUN ajst-27745 17 11 , , PUNCT ajst-27745 17 12 the the DET ajst-27745 17 13 length length NOUN ajst-27745 17 14 of of ADP ajst-27745 17 15 the the DET ajst-27745 17 16 dragon dragon NOUN ajst-27745 17 17 's 's PART ajst-27745 17 18 body body NOUN ajst-27745 17 19 and and CCONJ ajst-27745 17 20 tail tail NOUN ajst-27745 17 21 is be AUX ajst-27745 17 22 220 220 NUM ajst-27745 17 23 cm cm NOUN ajst-27745 17 24 , , PUNCT ajst-27745 17 25 and and CCONJ ajst-27745 17 26 the the DET ajst-27745 17 27 width width NOUN ajst-27745 17 28 of of ADP ajst-27745 17 29 all all DET ajst-27745 17 30 the the DET ajst-27745 17 31 benches bench NOUN ajst-27745 17 32 is be AUX ajst-27745 17 33 30 30 NUM ajst-27745 17 34 cm cm NOUN ajst-27745 17 35 . . PUNCT ajst-27745 18 1 each each DET ajst-27745 18 2 bench bench NOUN ajst-27745 18 3 has have VERB ajst-27745 18 4 two two NUM ajst-27745 18 5 holes hole NOUN ajst-27745 18 6 , , PUNCT ajst-27745 18 7 the the DET ajst-27745 18 8 diameter diameter NOUN ajst-27745 18 9 of of ADP ajst-27745 18 10 which which PRON ajst-27745 18 11 is be AUX ajst-27745 18 12 5.5 5.5 NUM ajst-27745 18 13 cm cm NOUN ajst-27745 18 14 , , PUNCT ajst-27745 18 15 and and CCONJ ajst-27745 18 16 the the DET ajst-27745 18 17 centre centre NOUN ajst-27745 18 18 of of ADP ajst-27745 18 19 the the DET ajst-27745 18 20 hole hole NOUN ajst-27745 18 21 is be AUX ajst-27745 18 22 27.5 27.5 NUM ajst-27745 18 23 cm cm NOUN ajst-27745 18 24 away away ADV ajst-27745 18 25 from from ADP ajst-27745 18 26 the the DET ajst-27745 18 27 head head NOUN ajst-27745 18 28 of of ADP ajst-27745 18 29 the the DET ajst-27745 18 30 nearest near ADJ ajst-27745 18 31 bench bench NOUN ajst-27745 18 32 . . PUNCT ajst-27745 19 1 the the DET ajst-27745 19 2 two two NUM ajst-27745 19 3 adjacent adjacent ADJ ajst-27745 19 4 benches bench NOUN ajst-27745 19 5 are be AUX ajst-27745 19 6 connected connect VERB ajst-27745 19 7 by by ADP ajst-27745 19 8 a a DET ajst-27745 19 9 handle handle NOUN ajst-27745 19 10 , , PUNCT ajst-27745 19 11 and and CCONJ ajst-27745 19 12 the the DET ajst-27745 19 13 two two NUM ajst-27745 19 14 benches bench NOUN ajst-27745 19 15 are be AUX ajst-27745 19 16 connected connect VERB ajst-27745 19 17 by by ADP ajst-27745 19 18 a a DET ajst-27745 19 19 handle handle NOUN ajst-27745 19 20 , , PUNCT ajst-27745 19 21 and and CCONJ ajst-27745 19 22 the the DET ajst-27745 19 23 two two NUM ajst-27745 19 24 benches bench NOUN ajst-27745 19 25 are be AUX ajst-27745 19 26 connected connect VERB ajst-27745 19 27 by by ADP ajst-27745 19 28 a a DET ajst-27745 19 29 handle handle NOUN ajst-27745 19 30 . . PUNCT ajst-27745 20 1 according accord VERB ajst-27745 20 2 to to ADP ajst-27745 20 3 the the DET ajst-27745 20 4 research research NOUN ajst-27745 20 5 , , PUNCT ajst-27745 20 6 the the DET ajst-27745 20 7 dragon dragon NOUN ajst-27745 20 8 dance dance NOUN ajst-27745 20 9 team team NOUN ajst-27745 20 10 coils coil NOUN ajst-27745 20 11 in in ADP ajst-27745 20 12 clockwise clockwise NOUN ajst-27745 20 13 along along ADP ajst-27745 20 14 an an DET ajst-27745 20 15 isometric isometric ADJ ajst-27745 20 16 solenoid solenoid NOUN ajst-27745 20 17 with with ADP ajst-27745 20 18 a a DET ajst-27745 20 19 pitch pitch NOUN ajst-27745 20 20 of of ADP ajst-27745 20 21 55 55 NUM ajst-27745 20 22 cm cm NOUN ajst-27745 20 23 , , PUNCT ajst-27745 20 24 and and CCONJ ajst-27745 20 25 the the DET ajst-27745 20 26 center center NOUN ajst-27745 20 27 of of ADP ajst-27745 20 28 each each DET ajst-27745 20 29 handle handle NOUN ajst-27745 20 30 is be AUX ajst-27745 20 31 located locate VERB ajst-27745 20 32 on on ADP ajst-27745 20 33 the the DET ajst-27745 20 34 solenoid solenoid NOUN ajst-27745 20 35 . . PUNCT ajst-27745 21 1 the the DET ajst-27745 21 2 traveling travel VERB ajst-27745 21 3 speed speed NOUN ajst-27745 21 4 of of ADP ajst-27745 21 5 the the DET ajst-27745 21 6 handles handle NOUN ajst-27745 21 7 in in ADP ajst-27745 21 8 front front NOUN ajst-27745 21 9 of of ADP ajst-27745 21 10 the the DET ajst-27745 21 11 dragon dragon NOUN ajst-27745 21 12 head head NOUN ajst-27745 21 13 is be AUX ajst-27745 21 14 always always ADV ajst-27745 21 15 1 1 NUM ajst-27745 21 16 m m NOUN ajst-27745 21 17 / / SYM ajst-27745 21 18 s. s. PROPN ajst-27745 21 19 after after ADP ajst-27745 21 20 consulting consult VERB ajst-27745 21 21 the the DET ajst-27745 21 22 information information NOUN ajst-27745 21 23 , , PUNCT ajst-27745 21 24 the the DET ajst-27745 21 25 thread thread NOUN ajst-27745 21 26 belongs belong VERB ajst-27745 21 27 to to ADP ajst-27745 21 28 the the DET ajst-27745 21 29 isometric isometric ADJ ajst-27745 21 30 thread thread NOUN ajst-27745 21 31 and and CCONJ ajst-27745 21 32 the the DET ajst-27745 21 33 general general ADJ ajst-27745 21 34 expression expression NOUN ajst-27745 21 35 can can AUX ajst-27745 21 36 be be AUX ajst-27745 21 37 given give VERB ajst-27745 21 38 by by ADP ajst-27745 21 39 the the DET ajst-27745 21 40 following follow VERB ajst-27745 21 41 equation equation NOUN ajst-27745 21 42 : : PUNCT ajst-27745 21 43 𝜌 𝜌 PUNCT ajst-27745 21 44 𝜌 𝜌 X ajst-27745 21 45 π‘πœƒ π‘πœƒ X ajst-27745 21 46 ( ( PUNCT ajst-27745 21 47 1 1 NUM ajst-27745 21 48 ) ) PUNCT ajst-27745 21 49 where where SCONJ ajst-27745 21 50 , , PUNCT ajst-27745 21 51 𝜌0 𝜌0 PROPN ajst-27745 21 52 , , PUNCT ajst-27745 21 53 πœƒ πœƒ X ajst-27745 21 54 are be AUX ajst-27745 21 55 the the DET ajst-27745 21 56 parameters parameter NOUN ajst-27745 21 57 to to PART ajst-27745 21 58 be be AUX ajst-27745 21 59 solved solve VERB ajst-27745 21 60 . . PUNCT ajst-27745 22 1 after after ADP ajst-27745 22 2 that that PRON ajst-27745 22 3 , , PUNCT ajst-27745 22 4 firstly firstly ADV ajst-27745 22 5 , , PUNCT ajst-27745 22 6 from from ADP ajst-27745 22 7 the the DET ajst-27745 22 8 known know VERB ajst-27745 22 9 parameter parameter NOUN ajst-27745 22 10 conditions condition NOUN ajst-27745 22 11 , , PUNCT ajst-27745 22 12 the the DET ajst-27745 22 13 pitch pitch NOUN ajst-27745 22 14 is be AUX ajst-27745 22 15 55 55 NUM ajst-27745 22 16 cm cm NOUN ajst-27745 22 17 , , PUNCT ajst-27745 22 18 πœƒ πœƒ X ajst-27745 22 19 > > X ajst-27745 22 20 0 0 NUM ajst-27745 22 21 , , PUNCT ajst-27745 22 22 the the DET ajst-27745 22 23 isometric isometric ADJ ajst-27745 22 24 solenoid solenoid NOUN ajst-27745 22 25 with with ADP ajst-27745 22 26 counterclockwise counterclockwise NOUN ajst-27745 22 27 positive positive ADJ ajst-27745 22 28 direction direction NOUN ajst-27745 22 29 centered center VERB ajst-27745 22 30 at at ADP ajst-27745 22 31 point point NOUN ajst-27745 22 32 𝑂 𝑂 PROPN ajst-27745 22 33 is be AUX ajst-27745 22 34 established establish VERB ajst-27745 22 35 , , PUNCT ajst-27745 22 36 and and CCONJ ajst-27745 22 37 the the DET ajst-27745 22 38 parametric parametric ADJ ajst-27745 22 39 equation equation NOUN ajst-27745 22 40 of of ADP ajst-27745 22 41 the the DET ajst-27745 22 42 solenoid solenoid NOUN ajst-27745 22 43 is be AUX ajst-27745 22 44 : : PUNCT ajst-27745 22 45 𝜌 𝜌 ADP ajst-27745 22 46 πœƒ πœƒ X ajst-27745 22 47 ( ( PUNCT ajst-27745 22 48 2 2 NUM ajst-27745 22 49 ) ) PUNCT ajst-27745 22 50 since since SCONJ ajst-27745 22 51 the the DET ajst-27745 22 52 subsequent subsequent ADJ ajst-27745 22 53 modeling modeling NOUN ajst-27745 22 54 process process NOUN ajst-27745 22 55 requires require VERB ajst-27745 22 56 the the DET ajst-27745 22 57 use use NOUN ajst-27745 22 58 of of ADP ajst-27745 22 59 the the DET ajst-27745 22 60 arc arc NOUN ajst-27745 22 61 length length NOUN ajst-27745 22 62 formula formula NOUN ajst-27745 22 63 in in ADP ajst-27745 22 64 isometric isometric ADJ ajst-27745 22 65 solenoids solenoid NOUN ajst-27745 22 66 , , PUNCT ajst-27745 22 67 the the DET ajst-27745 22 68 arc arc NOUN ajst-27745 22 69 length length NOUN ajst-27745 22 70 formula formula NOUN ajst-27745 22 71 is be AUX ajst-27745 22 72 derived derive VERB ajst-27745 22 73 by by ADP ajst-27745 22 74 line line NOUN ajst-27745 22 75 integration integration NOUN ajst-27745 22 76 , , PUNCT ajst-27745 22 77 and and CCONJ ajst-27745 22 78 the the DET ajst-27745 22 79 derivation derivation NOUN ajst-27745 22 80 process process NOUN ajst-27745 22 81 is be AUX ajst-27745 22 82 shown show VERB ajst-27745 22 83 below below ADP ajst-27745 22 84 , , PUNCT ajst-27745 22 85 which which PRON ajst-27745 22 86 takes take VERB ajst-27745 22 87 a a DET ajst-27745 22 88 combination combination NOUN ajst-27745 22 89 of of ADP ajst-27745 22 90 differential differential ADJ ajst-27745 22 91 and and CCONJ ajst-27745 22 92 integral integral ADJ ajst-27745 22 93 methods method NOUN ajst-27745 22 94 for for ADP ajst-27745 22 95 the the DET ajst-27745 22 96 derivation derivation NOUN ajst-27745 22 97 : : PUNCT ajst-27745 22 98 𝑑𝑠 𝑑𝑠 NOUN ajst-27745 22 99 π‘Žπœƒπ‘‘πœƒ π‘Žπœƒπ‘‘πœƒ VERB ajst-27745 22 100 π‘Žπ‘‘πœƒ π‘Žπ‘‘πœƒ VERB ajst-27745 22 101 π‘Žπœƒ π‘Žπœƒ PROPN ajst-27745 22 102 π‘Ž π‘Ž PROPN ajst-27745 22 103 π‘‘πœƒ π‘‘πœƒ PROPN ajst-27745 22 104 ( ( PUNCT ajst-27745 22 105 3 3 X ajst-27745 22 106 ) ) PUNCT ajst-27745 22 107 √𝐴 √𝐴 NOUN ajst-27745 23 1 𝐡π‘₯ 𝐡π‘₯ PROPN ajst-27745 23 2 𝐢π‘₯ 𝐢π‘₯ ADV ajst-27745 23 3 𝑑π‘₯ 𝑑π‘₯ VERB ajst-27745 23 4 ( ( PUNCT ajst-27745 23 5 4 4 NUM ajst-27745 23 6 ) ) PUNCT ajst-27745 23 7 integrating integrate VERB ajst-27745 23 8 both both DET ajst-27745 23 9 sides side NOUN ajst-27745 23 10 simultaneously simultaneously ADV ajst-27745 23 11 and and CCONJ ajst-27745 23 12 applying apply VERB ajst-27745 23 13 the the DET ajst-27745 23 14 integral integral ADJ ajst-27745 23 15 formula formula NOUN ajst-27745 23 16 yields yield NOUN ajst-27745 23 17 : : PUNCT ajst-27745 23 18 𝑑π‘₯ 𝑑π‘₯ ADP ajst-27745 23 19 𝐴 𝐴 PROPN ajst-27745 23 20 𝐡π‘₯ 𝐡π‘₯ PROPN ajst-27745 23 21 𝐢π‘₯2 𝐢π‘₯2 NOUN ajst-27745 23 22 1 1 NUM ajst-27745 23 23 √𝐢 √𝐢 NOUN ajst-27745 23 24 arcsinh arcsinh NOUN ajst-27745 23 25 2𝐢π‘₯ 2𝐢π‘₯ NUM ajst-27745 23 26 𝐡 𝐡 NOUN ajst-27745 23 27 4𝐴𝐢 4𝐴𝐢 NUM ajst-27745 23 28 𝐡2 𝐡2 NOUN ajst-27745 23 29 ( ( PUNCT ajst-27745 23 30 5 5 NUM ajst-27745 23 31 ) ) PUNCT ajst-27745 23 32 298 298 NUM ajst-27745 23 33 the the DET ajst-27745 23 34 final final ADJ ajst-27745 23 35 derived derived ADJ ajst-27745 23 36 equation equation NOUN ajst-27745 23 37 for for ADP ajst-27745 23 38 the the DET ajst-27745 23 39 arc arc NOUN ajst-27745 23 40 length length NOUN ajst-27745 23 41 of of ADP ajst-27745 23 42 an an DET ajst-27745 23 43 isometric isometric ADJ ajst-27745 23 44 solenoid solenoid NOUN ajst-27745 23 45 is be AUX ajst-27745 23 46 as as SCONJ ajst-27745 23 47 follows follow VERB ajst-27745 23 48 : : PUNCT ajst-27745 23 49 𝐿 𝐿 PROPN ajst-27745 23 50 πœƒ πœƒ PROPN ajst-27745 23 51 β‹… β‹… PROPN ajst-27745 23 52 β‹… β‹… PROPN ajst-27745 23 53 β‹… β‹… PROPN ajst-27745 23 54 β‹… β‹… PROPN ajst-27745 23 55 𝜌 𝜌 ADP ajst-27745 23 56 𝑏 𝑏 PROPN ajst-27745 23 57 2 2 NUM ajst-27745 23 58 β‹… β‹… X ajst-27745 23 59 𝜌 𝜌 X ajst-27745 23 60 β‹… β‹… X ajst-27745 23 61 𝑏 𝑏 PROPN ajst-27745 23 62 β‹… β‹… PROPN ajst-27745 23 63 πœƒ πœƒ PUNCT ajst-27745 23 64 𝑏 𝑏 DET ajst-27745 23 65 β‹… β‹… PROPN ajst-27745 23 66 πœƒ πœƒ NUM ajst-27745 23 67 |𝑏| |𝑏| PROPN ajst-27745 23 68 2 2 NUM ajst-27745 23 69 β‹… β‹… NOUN ajst-27745 23 70 arcsinh arcsinh NOUN ajst-27745 23 71 𝜌0 𝜌0 PROPN ajst-27745 23 72 π‘β‹…πœƒ π‘β‹…πœƒ PROPN ajst-27745 23 73 𝑏 𝑏 PROPN ajst-27745 23 74 ( ( PUNCT ajst-27745 23 75 6 6 NUM ajst-27745 23 76 ) ) PUNCT ajst-27745 23 77 in in ADP ajst-27745 23 78 order order NOUN ajst-27745 23 79 to to PART ajst-27745 23 80 obtain obtain VERB ajst-27745 23 81 the the DET ajst-27745 23 82 speed speed NOUN ajst-27745 23 83 as as ADV ajst-27745 23 84 well well ADV ajst-27745 23 85 as as ADP ajst-27745 23 86 the the DET ajst-27745 23 87 position position NOUN ajst-27745 23 88 information information NOUN ajst-27745 23 89 of of ADP ajst-27745 23 90 each each DET ajst-27745 23 91 node node NOUN ajst-27745 23 92 of of ADP ajst-27745 23 93 the the DET ajst-27745 23 94 bench bench NOUN ajst-27745 23 95 dragon dragon NOUN ajst-27745 23 96 under under ADP ajst-27745 23 97 each each DET ajst-27745 23 98 moment moment NOUN ajst-27745 23 99 , , PUNCT ajst-27745 23 100 we we PRON ajst-27745 23 101 regard regard VERB ajst-27745 23 102 each each DET ajst-27745 23 103 boarding boarding NOUN ajst-27745 23 104 as as ADP ajst-27745 23 105 a a DET ajst-27745 23 106 robotic robotic ADJ ajst-27745 23 107 arm arm NOUN ajst-27745 23 108 , , PUNCT ajst-27745 23 109 and and CCONJ ajst-27745 23 110 regard regard VERB ajst-27745 23 111 the the DET ajst-27745 23 112 handle handle NOUN ajst-27745 23 113 as as ADP ajst-27745 23 114 a a DET ajst-27745 23 115 joint joint NOUN ajst-27745 23 116 , , PUNCT ajst-27745 23 117 to to PART ajst-27745 23 118 construct construct VERB ajst-27745 23 119 a a DET ajst-27745 23 120 more more ADV ajst-27745 23 121 intuitive intuitive ADJ ajst-27745 23 122 robotic robotic ADJ ajst-27745 23 123 arm arm NOUN ajst-27745 23 124 model model NOUN ajst-27745 23 125 , , PUNCT ajst-27745 23 126 and and CCONJ ajst-27745 23 127 the the DET ajst-27745 23 128 simulation simulation NOUN ajst-27745 23 129 model model NOUN ajst-27745 23 130 is be AUX ajst-27745 23 131 shown show VERB ajst-27745 23 132 in in ADP ajst-27745 23 133 figure figure NOUN ajst-27745 23 134 1 1 NUM ajst-27745 23 135 below below ADV ajst-27745 23 136 . . PUNCT ajst-27745 24 1 figure figure NOUN ajst-27745 24 2 1 1 NUM ajst-27745 24 3 . . PUNCT ajst-27745 24 4 simulation simulation NOUN ajst-27745 24 5 of of ADP ajst-27745 24 6 robotic robotic ADJ ajst-27745 24 7 arm arm NOUN ajst-27745 24 8 model model NOUN ajst-27745 24 9 for for ADP ajst-27745 24 10 this this DET ajst-27745 24 11 model model NOUN ajst-27745 24 12 , , PUNCT ajst-27745 24 13 each each DET ajst-27745 24 14 plateen plateen VERB ajst-27745 24 15 is be AUX ajst-27745 24 16 considered consider VERB ajst-27745 24 17 as as ADP ajst-27745 24 18 a a DET ajst-27745 24 19 linkage linkage NOUN ajst-27745 24 20 , , PUNCT ajst-27745 24 21 and and CCONJ ajst-27745 24 22 each each DET ajst-27745 24 23 linkage linkage NOUN ajst-27745 24 24 has have VERB ajst-27745 24 25 a a DET ajst-27745 24 26 length length NOUN ajst-27745 24 27 of of ADP ajst-27745 24 28 220 220 NUM ajst-27745 24 29 cm cm NOUN ajst-27745 24 30 ( ( PUNCT ajst-27745 24 31 dragon dragon NOUN ajst-27745 24 32 body body NOUN ajst-27745 24 33 ) ) PUNCT ajst-27745 24 34 or or CCONJ ajst-27745 24 35 341 341 NUM ajst-27745 24 36 cm cm NOUN ajst-27745 24 37 ( ( PUNCT ajst-27745 24 38 dragon dragon NOUN ajst-27745 24 39 head head PROPN ajst-27745 24 40 ) ) PUNCT ajst-27745 24 41 and and CCONJ ajst-27745 24 42 a a DET ajst-27745 24 43 width width NOUN ajst-27745 24 44 of of ADP ajst-27745 24 45 30 30 NUM ajst-27745 24 46 cm cm NOUN ajst-27745 24 47 . . PUNCT ajst-27745 25 1 each each DET ajst-27745 25 2 handle handle NOUN ajst-27745 25 3 is be AUX ajst-27745 25 4 represented represent VERB ajst-27745 25 5 as as ADP ajst-27745 25 6 a a DET ajst-27745 25 7 joint joint NOUN ajst-27745 25 8 , , PUNCT ajst-27745 25 9 and and CCONJ ajst-27745 25 10 all all DET ajst-27745 25 11 joints joint NOUN ajst-27745 25 12 are be AUX ajst-27745 25 13 confined confine VERB ajst-27745 25 14 to to ADP ajst-27745 25 15 isometric isometric ADJ ajst-27745 25 16 solenoids solenoid NOUN ajst-27745 25 17 in in ADP ajst-27745 25 18 the the DET ajst-27745 25 19 two two NUM ajst-27745 25 20 - - PUNCT ajst-27745 25 21 dimensional dimensional ADJ ajst-27745 25 22 plane plane NOUN ajst-27745 25 23 , , PUNCT ajst-27745 25 24 so so SCONJ ajst-27745 25 25 the the DET ajst-27745 25 26 problem problem NOUN ajst-27745 25 27 of of ADP ajst-27745 25 28 solving solve VERB ajst-27745 25 29 the the DET ajst-27745 25 30 motion motion NOUN ajst-27745 25 31 of of ADP ajst-27745 25 32 the the DET ajst-27745 25 33 handles handle NOUN ajst-27745 25 34 before before ADV ajst-27745 25 35 and and CCONJ ajst-27745 25 36 after after SCONJ ajst-27745 25 37 all all DET ajst-27745 25 38 the the DET ajst-27745 25 39 boards board NOUN ajst-27745 25 40 is be AUX ajst-27745 25 41 converted convert VERB ajst-27745 25 42 into into ADP ajst-27745 25 43 a a DET ajst-27745 25 44 multi multi ADJ ajst-27745 25 45 - - ADJ ajst-27745 25 46 joint joint ADJ ajst-27745 25 47 robot robot NOUN ajst-27745 25 48 arm arm NOUN ajst-27745 25 49 problem problem NOUN ajst-27745 25 50 . . PUNCT ajst-27745 26 1 for for ADP ajst-27745 26 2 such such DET ajst-27745 26 3 a a DET ajst-27745 26 4 robotic robotic ADJ ajst-27745 26 5 arm arm NOUN ajst-27745 26 6 model model NOUN ajst-27745 26 7 , , PUNCT ajst-27745 26 8 it it PRON ajst-27745 26 9 is be AUX ajst-27745 26 10 only only ADV ajst-27745 26 11 necessary necessary ADJ ajst-27745 26 12 to to PART ajst-27745 26 13 solve solve VERB ajst-27745 26 14 the the DET ajst-27745 26 15 position position NOUN ajst-27745 26 16 and and CCONJ ajst-27745 26 17 speed speed NOUN ajst-27745 26 18 of of ADP ajst-27745 26 19 the the DET ajst-27745 26 20 faucet faucet NOUN ajst-27745 26 21 joint joint NOUN ajst-27745 26 22 , , PUNCT ajst-27745 26 23 and and CCONJ ajst-27745 26 24 then then ADV ajst-27745 26 25 through through ADP ajst-27745 26 26 the the DET ajst-27745 26 27 recursive recursive ADJ ajst-27745 26 28 formula formula NOUN ajst-27745 26 29 of of ADP ajst-27745 26 30 speed speed NOUN ajst-27745 26 31 and and CCONJ ajst-27745 26 32 position position NOUN ajst-27745 26 33 between between ADP ajst-27745 26 34 the the DET ajst-27745 26 35 joints joint NOUN ajst-27745 26 36 , , PUNCT ajst-27745 26 37 the the DET ajst-27745 26 38 position position NOUN ajst-27745 26 39 and and CCONJ ajst-27745 26 40 speed speed NOUN ajst-27745 26 41 of of ADP ajst-27745 26 42 each each DET ajst-27745 26 43 joint joint NOUN ajst-27745 26 44 can can AUX ajst-27745 26 45 be be AUX ajst-27745 26 46 solved solve VERB ajst-27745 26 47 sequentially sequentially ADV ajst-27745 26 48 . . PUNCT ajst-27745 27 1 let let VERB ajst-27745 27 2 the the DET ajst-27745 27 3 angle angle NOUN ajst-27745 27 4 in in ADP ajst-27745 27 5 the the DET ajst-27745 27 6 isometric isometric ADJ ajst-27745 27 7 solenoid solenoid NOUN ajst-27745 27 8 corresponding correspond VERB ajst-27745 27 9 to to ADP ajst-27745 27 10 the the DET ajst-27745 27 11 faucet faucet NOUN ajst-27745 27 12 when when SCONJ ajst-27745 27 13 it it PRON ajst-27745 27 14 reaches reach VERB ajst-27745 27 15 a a DET ajst-27745 27 16 certain certain ADJ ajst-27745 27 17 position position NOUN ajst-27745 27 18 be be AUX ajst-27745 27 19 πœƒ πœƒ NOUN ajst-27745 27 20 , , PUNCT ajst-27745 27 21 the the DET ajst-27745 27 22 arc arc NOUN ajst-27745 27 23 length length NOUN ajst-27745 27 24 as as ADP ajst-27745 27 25 a a DET ajst-27745 27 26 function function NOUN ajst-27745 27 27 of of ADP ajst-27745 27 28 πœƒ πœƒ NOUN ajst-27745 27 29 be be AUX ajst-27745 27 30 𝐿 𝐿 PROPN ajst-27745 27 31 πœƒ πœƒ PROPN ajst-27745 27 32 , , PUNCT ajst-27745 27 33 and and CCONJ ajst-27745 27 34 the the DET ajst-27745 27 35 total total ADJ ajst-27745 27 36 arc arc NOUN ajst-27745 27 37 length length NOUN ajst-27745 27 38 be be AUX ajst-27745 27 39 𝐿0 𝐿0 VERB ajst-27745 27 40 . . PUNCT ajst-27745 28 1 for for ADP ajst-27745 28 2 the the DET ajst-27745 28 3 faucet faucet NOUN ajst-27745 28 4 , , PUNCT ajst-27745 28 5 its its PRON ajst-27745 28 6 velocity velocity NOUN ajst-27745 28 7 is be AUX ajst-27745 28 8 along along ADP ajst-27745 28 9 the the DET ajst-27745 28 10 tangential tangential ADJ ajst-27745 28 11 direction direction NOUN ajst-27745 28 12 of of ADP ajst-27745 28 13 the the DET ajst-27745 28 14 solenoid solenoid NOUN ajst-27745 28 15 , , PUNCT ajst-27745 28 16 with with ADP ajst-27745 28 17 a a DET ajst-27745 28 18 magnitude magnitude NOUN ajst-27745 28 19 of of ADP ajst-27745 28 20 𝑣0 𝑣0 PROPN ajst-27745 28 21 1 1 NUM ajst-27745 28 22 m/s m/s PROPN ajst-27745 28 23 . . PUNCT ajst-27745 29 1 therefore therefore ADV ajst-27745 29 2 , , PUNCT ajst-27745 29 3 the the DET ajst-27745 29 4 arc arc NOUN ajst-27745 29 5 length length NOUN ajst-27745 29 6 traveled travel VERB ajst-27745 29 7 by by ADP ajst-27745 29 8 the the DET ajst-27745 29 9 faucet faucet NOUN ajst-27745 29 10 is be AUX ajst-27745 29 11 equal equal ADJ ajst-27745 29 12 to to ADP ajst-27745 29 13 the the DET ajst-27745 29 14 total total ADJ ajst-27745 29 15 arc arc NOUN ajst-27745 29 16 length length NOUN ajst-27745 29 17 minus minus ADP ajst-27745 29 18 the the DET ajst-27745 29 19 tangential tangential ADJ ajst-27745 29 20 velocity velocity NOUN ajst-27745 29 21 times time NOUN ajst-27745 29 22 time time NOUN ajst-27745 29 23 , , PUNCT ajst-27745 29 24 so so CCONJ ajst-27745 29 25 the the DET ajst-27745 29 26 parametric parametric ADJ ajst-27745 29 27 equation equation NOUN ajst-27745 29 28 for for ADP ajst-27745 29 29 arc arc NOUN ajst-27745 29 30 length length NOUN ajst-27745 29 31 versus versus ADP ajst-27745 29 32 time time NOUN ajst-27745 29 33 can can AUX ajst-27745 29 34 be be AUX ajst-27745 29 35 derived derive VERB ajst-27745 29 36 as as ADP ajst-27745 29 37 : : PUNCT ajst-27745 29 38 𝐿 𝐿 PROPN ajst-27745 29 39 πœƒ πœƒ PROPN ajst-27745 29 40 𝐿 𝐿 PROPN ajst-27745 29 41 𝑣 𝑣 ADP ajst-27745 29 42 𝑑 𝑑 X ajst-27745 29 43 ( ( PUNCT ajst-27745 29 44 7 7 NUM ajst-27745 29 45 ) ) PUNCT ajst-27745 29 46 πœƒ πœƒ NOUN ajst-27745 29 47 πœƒ πœƒ NUM ajst-27745 29 48 𝑑 𝑑 X ajst-27745 29 49 ( ( PUNCT ajst-27745 29 50 8) 8) NUM ajst-27745 29 51 since since SCONJ ajst-27745 29 52 arc arc NOUN ajst-27745 29 53 length length NOUN ajst-27745 29 54 , , PUNCT ajst-27745 29 55 radian radian PROPN ajst-27745 29 56 are be AUX ajst-27745 29 57 functions function NOUN ajst-27745 29 58 of of ADP ajst-27745 29 59 time time NOUN ajst-27745 29 60 , , PUNCT ajst-27745 29 61 it it PRON ajst-27745 29 62 is be AUX ajst-27745 29 63 further far ADV ajst-27745 29 64 possible possible ADJ ajst-27745 29 65 to to PART ajst-27745 29 66 introduce introduce VERB ajst-27745 29 67 π‘₯ π‘₯ PROPN ajst-27745 29 68 𝑑 𝑑 PROPN ajst-27745 29 69 and and CCONJ ajst-27745 29 70 𝑦 𝑦 PROPN ajst-27745 29 71 𝑑 𝑑 PROPN ajst-27745 29 72 , , PUNCT ajst-27745 29 73 which which PRON ajst-27745 29 74 are be AUX ajst-27745 29 75 obtained obtain VERB ajst-27745 29 76 according accord VERB ajst-27745 29 77 to to ADP ajst-27745 29 78 the the DET ajst-27745 29 79 conversion conversion NOUN ajst-27745 29 80 relationship relationship NOUN ajst-27745 29 81 between between ADP ajst-27745 29 82 polar polar ADJ ajst-27745 29 83 and and CCONJ ajst-27745 29 84 cartesian cartesian ADJ ajst-27745 29 85 coordinates coordinate NOUN ajst-27745 29 86 : : PUNCT ajst-27745 29 87 π‘₯ π‘₯ NUM ajst-27745 29 88 𝑑 𝑑 X ajst-27745 29 89 𝜌 𝜌 X ajst-27745 29 90 𝑑 𝑑 X ajst-27745 29 91 cos cos PROPN ajst-27745 29 92 πœƒ πœƒ PROPN ajst-27745 29 93 𝑑 𝑑 X ajst-27745 29 94 𝑦 𝑦 NUM ajst-27745 29 95 𝑑 𝑑 X ajst-27745 29 96 𝜌 𝜌 ADP ajst-27745 29 97 𝑑 𝑑 ADP ajst-27745 29 98 sin sin NOUN ajst-27745 29 99 πœƒ πœƒ X ajst-27745 29 100 𝑑 𝑑 X ajst-27745 29 101 ( ( PUNCT ajst-27745 29 102 9 9 NUM ajst-27745 29 103 ) ) PUNCT ajst-27745 29 104 let let VERB ajst-27745 29 105 the the DET ajst-27745 29 106 position position NOUN ajst-27745 29 107 of of ADP ajst-27745 29 108 the the DET ajst-27745 29 109 dragon dragon NOUN ajst-27745 29 110 head head NOUN ajst-27745 29 111 be be AUX ajst-27745 29 112 π‘₯0 π‘₯0 PROPN ajst-27745 29 113 𝑑 𝑑 NOUN ajst-27745 29 114 , , PUNCT ajst-27745 29 115 𝑦0 𝑦0 PROPN ajst-27745 29 116 𝑑 𝑑 PROPN ajst-27745 29 117 , , PUNCT ajst-27745 29 118 the the DET ajst-27745 29 119 boarding boarding NOUN ajst-27745 29 120 length length NOUN ajst-27745 29 121 of of ADP ajst-27745 29 122 the the DET ajst-27745 29 123 dragon dragon NOUN ajst-27745 29 124 head head NOUN ajst-27745 29 125 be be AUX ajst-27745 29 126 𝐿0 𝐿0 VERB ajst-27745 29 127 286 286 NUM ajst-27745 29 128 cm cm NOUN ajst-27745 29 129 , , PUNCT ajst-27745 29 130 the the DET ajst-27745 29 131 position position NOUN ajst-27745 29 132 of of ADP ajst-27745 29 133 the the DET ajst-27745 29 134 dragon dragon NOUN ajst-27745 29 135 body body NOUN ajst-27745 29 136 of of ADP ajst-27745 29 137 the the DET ajst-27745 29 138 i i PROPN ajst-27745 29 139 - - PUNCT ajst-27745 29 140 th th X ajst-27745 29 141 section section NOUN ajst-27745 29 142 i i NOUN ajst-27745 29 143 1,2 1,2 NUM ajst-27745 29 144 , , PUNCT ajst-27745 29 145 … … PUNCT ajst-27745 29 146 222 222 NUM ajst-27745 29 147 ) ) PUNCT ajst-27745 29 148 be be VERB ajst-27745 29 149 π‘₯𝑖 π‘₯𝑖 ADP ajst-27745 29 150 𝑑 𝑑 PROPN ajst-27745 29 151 , , PUNCT ajst-27745 29 152 𝑦𝑖 𝑦𝑖 NUM ajst-27745 29 153 𝑑 𝑑 PROPN ajst-27745 29 154 , , PUNCT ajst-27745 29 155 and and CCONJ ajst-27745 29 156 the the DET ajst-27745 29 157 boarding boarding NOUN ajst-27745 29 158 length length NOUN ajst-27745 29 159 of of ADP ajst-27745 29 160 the the DET ajst-27745 29 161 dragon dragon NOUN ajst-27745 29 162 body body NOUN ajst-27745 29 163 be be AUX ajst-27745 29 164 𝐿1 𝐿1 PROPN ajst-27745 29 165 165 165 NUM ajst-27745 29 166 cm cm NOUN ajst-27745 29 167 , , PUNCT ajst-27745 29 168 so so SCONJ ajst-27745 29 169 that that SCONJ ajst-27745 29 170 the the DET ajst-27745 29 171 relationship relationship NOUN ajst-27745 29 172 of of ADP ajst-27745 29 173 the the DET ajst-27745 29 174 adjacent adjacent ADJ ajst-27745 29 175 joints joint NOUN ajst-27745 29 176 can can AUX ajst-27745 29 177 be be AUX ajst-27745 29 178 obtained obtain VERB ajst-27745 29 179 according accord VERB ajst-27745 29 180 to to ADP ajst-27745 29 181 the the DET ajst-27745 29 182 definition definition NOUN ajst-27745 29 183 of of ADP ajst-27745 29 184 euclidean euclidean ADJ ajst-27745 29 185 distance distance NOUN ajst-27745 29 186 : : PUNCT ajst-27745 29 187 π‘₯ π‘₯ NOUN ajst-27745 29 188 𝑑 𝑑 VERB ajst-27745 29 189 π‘₯ π‘₯ X ajst-27745 29 190 𝑑 𝑑 X ajst-27745 29 191 𝑦 𝑦 NUM ajst-27745 29 192 𝑑 𝑑 X ajst-27745 29 193 𝑦 𝑦 NUM ajst-27745 29 194 𝑑 𝑑 NOUN ajst-27745 29 195 𝐿 𝐿 PROPN ajst-27745 29 196 π‘₯ π‘₯ X ajst-27745 29 197 𝑑 𝑑 NOUN ajst-27745 29 198 π‘₯ π‘₯ NOUN ajst-27745 29 199 𝑑 𝑑 X ajst-27745 29 200 𝑦 𝑦 NUM ajst-27745 29 201 𝑑 𝑑 X ajst-27745 29 202 𝑦 𝑦 NUM ajst-27745 29 203 𝑑 𝑑 PRON ajst-27745 29 204 𝐿 𝐿 PROPN ajst-27745 29 205 𝑖 𝑖 PROPN ajst-27745 29 206 1,2 1,2 NUM ajst-27745 29 207 , , PUNCT ajst-27745 29 208 … … PUNCT ajst-27745 29 209 222 222 NUM ajst-27745 29 210 ( ( PUNCT ajst-27745 29 211 10 10 NUM ajst-27745 29 212 ) ) PUNCT ajst-27745 29 213 the the DET ajst-27745 29 214 position position NOUN ajst-27745 29 215 of of ADP ajst-27745 29 216 each each DET ajst-27745 29 217 joint joint NOUN ajst-27745 29 218 as as ADP ajst-27745 29 219 a a DET ajst-27745 29 220 function function NOUN ajst-27745 29 221 of of ADP ajst-27745 29 222 time time NOUN ajst-27745 29 223 can can AUX ajst-27745 29 224 be be AUX ajst-27745 29 225 obtained obtain VERB ajst-27745 29 226 by by ADP ajst-27745 29 227 combining combine VERB ajst-27745 29 228 the the DET ajst-27745 29 229 equations equation NOUN ajst-27745 29 230 of of ADP ajst-27745 29 231 the the DET ajst-27745 29 232 circle circle NOUN ajst-27745 29 233 centered center VERB ajst-27745 29 234 on on ADP ajst-27745 29 235 the the DET ajst-27745 29 236 joint joint NOUN ajst-27745 29 237 , , PUNCT ajst-27745 29 238 the the DET ajst-27745 29 239 equations equation NOUN ajst-27745 29 240 of of ADP ajst-27745 29 241 the the DET ajst-27745 29 242 parameters parameter NOUN ajst-27745 29 243 of of ADP ajst-27745 29 244 the the DET ajst-27745 29 245 solenoid solenoid NOUN ajst-27745 29 246 , , PUNCT ajst-27745 29 247 and and CCONJ ajst-27745 29 248 the the DET ajst-27745 29 249 equations equation NOUN ajst-27745 29 250 of of ADP ajst-27745 29 251 the the DET ajst-27745 29 252 polar polar ADJ ajst-27745 29 253 coordinates coordinate NOUN ajst-27745 29 254 , , PUNCT ajst-27745 29 255 i.e. i.e. X ajst-27745 29 256 , , PUNCT ajst-27745 29 257 equations equation NOUN ajst-27745 29 258 ( ( PUNCT ajst-27745 29 259 2 2 NUM ajst-27745 29 260 ) ) PUNCT ajst-27745 29 261 , , PUNCT ajst-27745 29 262 ( ( PUNCT ajst-27745 29 263 8) 8) NUM ajst-27745 29 264 , , PUNCT ajst-27745 29 265 and and CCONJ ajst-27745 29 266 ( ( PUNCT ajst-27745 29 267 9 9 NUM ajst-27745 29 268 ) ) PUNCT ajst-27745 29 269 , , PUNCT ajst-27745 29 270 being be AUX ajst-27745 29 271 careful careful ADJ ajst-27745 29 272 to to PART ajst-27745 29 273 limit limit VERB ajst-27745 29 274 the the DET ajst-27745 29 275 length length NOUN ajst-27745 29 276 of of ADP ajst-27745 29 277 the the DET ajst-27745 29 278 arcs arc NOUN ajst-27745 29 279 or or CCONJ ajst-27745 29 280 else else ADV ajst-27745 29 281 more more ADJ ajst-27745 29 282 than than ADP ajst-27745 29 283 one one NUM ajst-27745 29 284 solution solution NOUN ajst-27745 29 285 may may AUX ajst-27745 29 286 be be AUX ajst-27745 29 287 found find VERB ajst-27745 29 288 . . PUNCT ajst-27745 30 1 initially initially ADV ajst-27745 30 2 , , PUNCT ajst-27745 30 3 the the DET ajst-27745 30 4 faucet faucet NOUN ajst-27745 30 5 is be AUX ajst-27745 30 6 located locate VERB ajst-27745 30 7 at at ADP ajst-27745 30 8 point point NOUN ajst-27745 30 9 a a PRON ajst-27745 30 10 on on ADP ajst-27745 30 11 the the DET ajst-27745 30 12 16 16 NUM ajst-27745 30 13 - - PUNCT ajst-27745 30 14 th th NOUN ajst-27745 30 15 turn turn NOUN ajst-27745 30 16 of of ADP ajst-27745 30 17 the the DET ajst-27745 30 18 spiral spiral NOUN ajst-27745 30 19 , , PUNCT ajst-27745 30 20 and and CCONJ ajst-27745 30 21 this this DET ajst-27745 30 22 condition condition NOUN ajst-27745 30 23 is be AUX ajst-27745 30 24 used use VERB ajst-27745 30 25 to to PART ajst-27745 30 26 find find VERB ajst-27745 30 27 the the DET ajst-27745 30 28 required require VERB ajst-27745 30 29 position position NOUN ajst-27745 30 30 information information NOUN ajst-27745 30 31 . . PUNCT ajst-27745 31 1 figure figure NOUN ajst-27745 31 2 2 2 NUM ajst-27745 31 3 . . PUNCT ajst-27745 31 4 joint joint ADJ ajst-27745 31 5 velocity velocity NOUN ajst-27745 31 6 schematic schematic ADJ ajst-27745 31 7 figure figure NOUN ajst-27745 31 8 2 2 NUM ajst-27745 31 9 shows show VERB ajst-27745 31 10 the the DET ajst-27745 31 11 two two NUM ajst-27745 31 12 joints joint NOUN ajst-27745 31 13 before before ADP ajst-27745 31 14 and and CCONJ ajst-27745 31 15 after after ADP ajst-27745 31 16 boarding boarding NOUN ajst-27745 31 17 , , PUNCT ajst-27745 31 18 the the DET ajst-27745 31 19 back back ADJ ajst-27745 31 20 handle handle NOUN ajst-27745 31 21 of of ADP ajst-27745 31 22 the the DET ajst-27745 31 23 𝑖-th 𝑖-th PROPN ajst-27745 31 24 boarding boarding NOUN ajst-27745 31 25 is be AUX ajst-27745 31 26 also also ADV ajst-27745 31 27 the the DET ajst-27745 31 28 front front ADJ ajst-27745 31 29 handle handle NOUN ajst-27745 31 30 of of ADP ajst-27745 31 31 the the DET ajst-27745 31 32 ( ( PUNCT ajst-27745 31 33 𝑖 𝑖 SYM ajst-27745 31 34 1)-th 1)-th NUM ajst-27745 31 35 boarding boarding NOUN ajst-27745 31 36 , , PUNCT ajst-27745 31 37 πœƒ πœƒ PRON ajst-27745 31 38 represents represent VERB ajst-27745 31 39 the the DET ajst-27745 31 40 polar polar ADJ ajst-27745 31 41 angle angle NOUN ajst-27745 31 42 of of ADP ajst-27745 31 43 the the DET ajst-27745 31 44 back back ADJ ajst-27745 31 45 handle handle NOUN ajst-27745 31 46 of of ADP ajst-27745 31 47 the the DET ajst-27745 31 48 𝑖-th 𝑖-th PROPN ajst-27745 31 49 boarding boarding NOUN ajst-27745 31 50 , , PUNCT ajst-27745 31 51 πœƒ πœƒ PRON ajst-27745 31 52 represents represent VERB ajst-27745 31 53 the the DET ajst-27745 31 54 polar polar ADJ ajst-27745 31 55 angle angle NOUN ajst-27745 31 56 of of ADP ajst-27745 31 57 the the DET ajst-27745 31 58 back back ADJ ajst-27745 31 59 handle handle NOUN ajst-27745 31 60 of of ADP ajst-27745 31 61 the the DET ajst-27745 31 62 ( ( PUNCT ajst-27745 31 63 𝑖 𝑖 SYM ajst-27745 31 64 1)st 1)st NUM ajst-27745 31 65 boarding boarding NOUN ajst-27745 31 66 , , PUNCT ajst-27745 31 67 𝛽 𝛽 NOUN ajst-27745 31 68 represents represent VERB ajst-27745 31 69 the the DET ajst-27745 31 70 difference difference NOUN ajst-27745 31 71 of of ADP ajst-27745 31 72 the the DET ajst-27745 31 73 polar polar ADJ ajst-27745 31 74 angles angle NOUN ajst-27745 31 75 , , PUNCT ajst-27745 31 76 𝑇 𝑇 PROPN ajst-27745 31 77 , , PUNCT ajst-27745 31 78 𝑅 𝑅 PROPN ajst-27745 31 79 represent represent VERB ajst-27745 31 80 the the DET ajst-27745 31 81 tangential tangential ADJ ajst-27745 31 82 and and CCONJ ajst-27745 31 83 radial radial ADJ ajst-27745 31 84 vectors vector NOUN ajst-27745 31 85 , , PUNCT ajst-27745 31 86 and and CCONJ ajst-27745 31 87 the the DET ajst-27745 31 88 direction direction NOUN ajst-27745 31 89 of of ADP ajst-27745 31 90 the the DET ajst-27745 31 91 velocity velocity NOUN ajst-27745 31 92 on on ADP ajst-27745 31 93 the the DET ajst-27745 31 94 spiral spiral ADJ ajst-27745 31 95 οΏ½ οΏ½ NOUN ajst-27745 31 96 βƒ— βƒ— NOUN ajst-27745 31 97 οΏ½ οΏ½ PROPN ajst-27745 31 98 is be AUX ajst-27745 31 99 in in ADP ajst-27745 31 100 the the DET ajst-27745 31 101 same same ADJ ajst-27745 31 102 direction direction NOUN ajst-27745 31 103 as as ADP ajst-27745 31 104 οΏ½ οΏ½ PROPN ajst-27745 31 105 βƒ— βƒ— PART ajst-27745 31 106 οΏ½ οΏ½ PROPN ajst-27745 31 107 . . PUNCT ajst-27745 32 1 in in ADP ajst-27745 32 2 this this DET ajst-27745 32 3 paper paper NOUN ajst-27745 32 4 , , PUNCT ajst-27745 32 5 the the DET ajst-27745 32 6 angle angle NOUN ajst-27745 32 7 between between ADP ajst-27745 32 8 each each DET ajst-27745 32 9 velocity velocity NOUN ajst-27745 32 10 and and CCONJ ajst-27745 32 11 the the DET ajst-27745 32 12 rod rod NOUN ajst-27745 32 13 is be AUX ajst-27745 32 14 calculated calculate VERB ajst-27745 32 15 , , PUNCT ajst-27745 32 16 and and CCONJ ajst-27745 32 17 the the DET ajst-27745 32 18 velocities velocity NOUN ajst-27745 32 19 at at ADP ajst-27745 32 20 each each DET ajst-27745 32 21 joint joint NOUN ajst-27745 32 22 are be AUX ajst-27745 32 23 solved solve VERB ajst-27745 32 24 recursively recursively ADV ajst-27745 32 25 . . PUNCT ajst-27745 33 1 checking check VERB ajst-27745 33 2 the the DET ajst-27745 33 3 literature literature NOUN ajst-27745 33 4 , , PUNCT ajst-27745 33 5 it it PRON ajst-27745 33 6 can can AUX ajst-27745 33 7 be be AUX ajst-27745 33 8 obtained obtain VERB ajst-27745 33 9 that that PRON ajst-27745 33 10 for for ADP ajst-27745 33 11 any any DET ajst-27745 33 12 point point NOUN ajst-27745 33 13 𝑃 𝑃 NOUN ajst-27745 33 14 on on ADP ajst-27745 33 15 the the DET ajst-27745 33 16 solenoid solenoid NOUN ajst-27745 33 17 , , PUNCT ajst-27745 33 18 its its PRON ajst-27745 33 19 tangential tangential ADJ ajst-27745 33 20 vector vector NOUN ajst-27745 33 21 consists consist VERB ajst-27745 33 22 of of ADP ajst-27745 33 23 the the DET ajst-27745 33 24 parameters parameter NOUN ajst-27745 33 25 of of ADP ajst-27745 33 26 the the DET ajst-27745 33 27 solenoid solenoid ADJ ajst-27745 33 28 equation equation NOUN ajst-27745 33 29 , , PUNCT ajst-27745 33 30 and and CCONJ ajst-27745 33 31 let let VERB ajst-27745 33 32 the the DET ajst-27745 33 33 tangential tangential ADJ ajst-27745 33 34 vector vector NOUN ajst-27745 33 35 at at ADP ajst-27745 33 36 the the DET ajst-27745 33 37 point point NOUN ajst-27745 33 38 be be AUX ajst-27745 33 39 οΏ½ οΏ½ NOUN ajst-27745 33 40 βƒ— βƒ— NOUN ajst-27745 33 41 οΏ½ οΏ½ PROPN ajst-27745 33 42 𝑇 𝑇 PROPN ajst-27745 33 43 , , PUNCT ajst-27745 33 44 𝑇 𝑇 PROPN ajst-27745 33 45 t t PROPN ajst-27745 33 46 βƒ—_𝑖=(𝑇 βƒ—_𝑖=(𝑇 PROPN ajst-27745 33 47 , , PUNCT ajst-27745 33 48 𝑇 𝑇 PROPN ajst-27745 33 49 ) ) PUNCT ajst-27745 33 50 , , PUNCT ajst-27745 33 51 then then ADV ajst-27745 33 52 the the DET ajst-27745 33 53 tangential tangential ADJ ajst-27745 33 54 vector vector NOUN ajst-27745 33 55 is be AUX ajst-27745 33 56 given give VERB ajst-27745 33 57 by by ADP ajst-27745 33 58 the the DET ajst-27745 33 59 following follow VERB ajst-27745 33 60 equation equation NOUN ajst-27745 33 61 : : PUNCT ajst-27745 33 62 𝑇 𝑇 PROPN ajst-27745 33 63 𝑏 𝑏 PROPN ajst-27745 33 64 β‹… β‹… PROPN ajst-27745 33 65 cos cos PROPN ajst-27745 33 66 πœƒ πœƒ X ajst-27745 33 67 𝜌 𝜌 X ajst-27745 33 68 𝑏 𝑏 PROPN ajst-27745 33 69 β‹… β‹… PROPN ajst-27745 33 70 πœƒ πœƒ PROPN ajst-27745 33 71 sin sin VERB ajst-27745 34 1 πœƒ πœƒ NOUN ajst-27745 34 2 𝑇 𝑇 NOUN ajst-27745 35 1 𝑏 𝑏 PROPN ajst-27745 35 2 β‹… β‹… PROPN ajst-27745 35 3 sin sin NOUN ajst-27745 35 4 πœƒ πœƒ X ajst-27745 35 5 𝜌 𝜌 X ajst-27745 35 6 𝑏 𝑏 PROPN ajst-27745 35 7 β‹… β‹… PROPN ajst-27745 35 8 πœƒ πœƒ PROPN ajst-27745 35 9 cos cos PROPN ajst-27745 35 10 πœƒ πœƒ X ajst-27745 35 11 ( ( PUNCT ajst-27745 35 12 11 11 NUM ajst-27745 35 13 ) ) PUNCT ajst-27745 35 14 for for ADP ajst-27745 35 15 the the DET ajst-27745 35 16 𝑖-th 𝑖-th PROPN ajst-27745 35 17 joint joint NOUN ajst-27745 35 18 , , PUNCT ajst-27745 35 19 the the DET ajst-27745 35 20 vector vector NOUN ajst-27745 35 21 pointing pointing NOUN ajst-27745 35 22 to to ADP ajst-27745 35 23 the the DET ajst-27745 35 24 next next ADJ ajst-27745 35 25 joint joint NOUN ajst-27745 35 26 is be AUX ajst-27745 35 27 𝑅 𝑅 PROPN ajst-27745 35 28 π‘₯ π‘₯ VERB ajst-27745 35 29 π‘₯ π‘₯ X ajst-27745 35 30 , , PUNCT ajst-27745 35 31 𝑦 𝑦 NOUN ajst-27745 35 32 𝑦 𝑦 NOUN ajst-27745 35 33 , , PUNCT ajst-27745 35 34 so so CCONJ ajst-27745 35 35 for for ADP ajst-27745 35 36 finding find VERB ajst-27745 35 37 the the DET ajst-27745 35 38 angle angle NOUN ajst-27745 35 39 𝛼 𝛼 INTJ ajst-27745 35 40 , , PUNCT ajst-27745 35 41 it it PRON ajst-27745 35 42 is be AUX ajst-27745 35 43 simpler simple ADJ ajst-27745 35 44 to to PART ajst-27745 35 45 find find VERB ajst-27745 35 46 the the DET ajst-27745 35 47 angle angle NOUN ajst-27745 35 48 of of ADP ajst-27745 35 49 the the DET ajst-27745 35 50 two two NUM ajst-27745 35 51 vectors vector NOUN ajst-27745 35 52 i.e. i.e. X ajst-27745 35 53 𝛼 𝛼 X ajst-27745 35 54 arccos arccos X ajst-27745 35 55 βƒ— βƒ— PROPN ajst-27745 35 56 β‹… β‹… PROPN ajst-27745 35 57 βƒ— βƒ— PROPN ajst-27745 35 58 βƒ— βƒ— X ajst-27745 35 59 βƒ— βƒ— PROPN ajst-27745 35 60 ( ( PUNCT ajst-27745 35 61 12 12 NUM ajst-27745 35 62 ) ) PUNCT ajst-27745 35 63 299 299 NUM ajst-27745 35 64 the the DET ajst-27745 35 65 link link NOUN ajst-27745 35 66 between between ADP ajst-27745 35 67 the the DET ajst-27745 35 68 forward forward ADJ ajst-27745 35 69 and and CCONJ ajst-27745 35 70 backward backward ADJ ajst-27745 35 71 velocities velocity NOUN ajst-27745 35 72 is be AUX ajst-27745 35 73 given give VERB ajst-27745 35 74 by by ADP ajst-27745 35 75 the the DET ajst-27745 35 76 recursive recursive ADJ ajst-27745 35 77 modeling modeling NOUN ajst-27745 35 78 of of ADP ajst-27745 35 79 the the DET ajst-27745 35 80 velocities velocity NOUN ajst-27745 35 81 of of ADP ajst-27745 35 82 this this DET ajst-27745 35 83 joint joint NOUN ajst-27745 35 84 : : PUNCT ajst-27745 35 85 𝑣 𝑣 AUX ajst-27745 35 86 β‹… β‹… PROPN ajst-27745 35 87 𝛼 𝛼 VERB ajst-27745 35 88 𝑣 𝑣 PROPN ajst-27745 35 89 β‹… β‹… PROPN ajst-27745 35 90 𝛼 𝛼 X ajst-27745 35 91 ( ( PUNCT ajst-27745 35 92 13 13 NUM ajst-27745 35 93 ) ) PUNCT ajst-27745 35 94 therefore therefore ADV ajst-27745 35 95 , , PUNCT ajst-27745 35 96 the the DET ajst-27745 35 97 1 1 NUM ajst-27745 35 98 m/s m/s NOUN ajst-27745 35 99 of of ADP ajst-27745 35 100 the the DET ajst-27745 35 101 dragon dragon NOUN ajst-27745 35 102 's 's PART ajst-27745 35 103 head head NOUN ajst-27745 35 104 can can AUX ajst-27745 35 105 be be AUX ajst-27745 35 106 used use VERB ajst-27745 35 107 to to PART ajst-27745 35 108 solve solve VERB ajst-27745 35 109 the the DET ajst-27745 35 110 speed speed NOUN ajst-27745 35 111 of of ADP ajst-27745 35 112 the the DET ajst-27745 35 113 back back ADJ ajst-27745 35 114 part part NOUN ajst-27745 35 115 of of ADP ajst-27745 35 116 the the DET ajst-27745 35 117 handle handle NOUN ajst-27745 35 118 by by ADP ajst-27745 35 119 iterative iterative NOUN ajst-27745 35 120 recursion recursion NOUN ajst-27745 35 121 . . PUNCT ajst-27745 36 1 the the DET ajst-27745 36 2 horizontal horizontal ADJ ajst-27745 36 3 and and CCONJ ajst-27745 36 4 vertical vertical ADJ ajst-27745 36 5 coordinate coordinate NOUN ajst-27745 36 6 positions position NOUN ajst-27745 36 7 of of ADP ajst-27745 36 8 the the DET ajst-27745 36 9 dragon dragon NOUN ajst-27745 36 10 dance dance NOUN ajst-27745 36 11 team team NOUN ajst-27745 36 12 at at ADP ajst-27745 36 13 each each DET ajst-27745 36 14 moment moment NOUN ajst-27745 36 15 are be AUX ajst-27745 36 16 given give VERB ajst-27745 36 17 in in ADP ajst-27745 36 18 table table NOUN ajst-27745 36 19 1 1 NUM ajst-27745 36 20 below below ADV ajst-27745 36 21 , , PUNCT ajst-27745 36 22 and and CCONJ ajst-27745 36 23 the the DET ajst-27745 36 24 speed speed NOUN ajst-27745 36 25 of of ADP ajst-27745 36 26 the the DET ajst-27745 36 27 dragon dragon NOUN ajst-27745 36 28 dance dance NOUN ajst-27745 36 29 team team NOUN ajst-27745 36 30 at at ADP ajst-27745 36 31 each each DET ajst-27745 36 32 moment moment NOUN ajst-27745 36 33 is be AUX ajst-27745 36 34 given give VERB ajst-27745 36 35 in in ADP ajst-27745 36 36 table table NOUN ajst-27745 36 37 2 2 NUM ajst-27745 36 38 below below ADV ajst-27745 36 39 . . PUNCT ajst-27745 37 1 table table NOUN ajst-27745 37 2 1 1 NUM ajst-27745 37 3 . . PUNCT ajst-27745 37 4 horizontal horizontal ADJ ajst-27745 37 5 and and CCONJ ajst-27745 37 6 vertical vertical ADJ ajst-27745 37 7 coordinates coordinate NOUN ajst-27745 37 8 of of ADP ajst-27745 37 9 the the DET ajst-27745 37 10 position position NOUN ajst-27745 37 11 of of ADP ajst-27745 37 12 the the DET ajst-27745 37 13 dragon dragon NOUN ajst-27745 37 14 dance dance NOUN ajst-27745 37 15 team team NOUN ajst-27745 37 16 at at ADP ajst-27745 37 17 each each DET ajst-27745 37 18 moment moment NOUN ajst-27745 37 19 in in ADP ajst-27745 37 20 time time NOUN ajst-27745 37 21 0 0 NUM ajst-27745 37 22 s s PART ajst-27745 38 1 60 60 NUM ajst-27745 38 2 s s NOUN ajst-27745 38 3 120 120 NUM ajst-27745 38 4 s s NUM ajst-27745 38 5 180 180 NUM ajst-27745 38 6 s s NUM ajst-27745 38 7 240 240 NUM ajst-27745 38 8 s s NUM ajst-27745 38 9 300 300 NUM ajst-27745 38 10 s s NOUN ajst-27745 38 11 mixer mixer NOUN ajst-27745 38 12 x x SYM ajst-27745 38 13 ( ( PUNCT ajst-27745 38 14 m m NOUN ajst-27745 38 15 ) ) PUNCT ajst-27745 38 16 8.800000 8.800000 NUM ajst-27745 38 17 5.662178 5.662178 NUM ajst-27745 38 18 4.453844 4.453844 NUM ajst-27745 38 19 2.327034 2.327034 NUM ajst-27745 38 20 2.351795 2.351795 NUM ajst-27745 38 21 4.699969 4.699969 NUM ajst-27745 38 22 mixer mixer NOUN ajst-27745 38 23 y y PROPN ajst-27745 38 24 ( ( PUNCT ajst-27745 38 25 m m PROPN ajst-27745 38 26 ) ) PUNCT ajst-27745 38 27 0 0 PUNCT ajst-27745 38 28 -5.902779 -5.902779 PROPN ajst-27745 39 1 6.042917 6.042917 NUM ajst-27745 39 2 6.355608 6.355608 NUM ajst-27745 39 3 5.463400 5.463400 NUM ajst-27745 39 4 1.644806 1.644806 NUM ajst-27745 39 5 section section NOUN ajst-27745 39 6 1 1 NUM ajst-27745 39 7 of of ADP ajst-27745 39 8 the the DET ajst-27745 39 9 dragon dragon NOUN ajst-27745 39 10 's 's PART ajst-27745 39 11 body body NOUN ajst-27745 39 12 x x SYM ajst-27745 39 13 ( ( PUNCT ajst-27745 39 14 m m NOUN ajst-27745 39 15 ) ) PUNCT ajst-27745 39 16 7.372824 7.372824 NUM ajst-27745 39 17 1.886354 1.886354 NUM ajst-27745 39 18 4.763584 4.763584 NUM ajst-27745 39 19 4.655571 4.655571 NUM ajst-27745 39 20 3.063900 3.063900 NUM ajst-27745 39 21 section section NOUN ajst-27745 39 22 1 1 NUM ajst-27745 39 23 of of ADP ajst-27745 39 24 the the DET ajst-27745 39 25 dragon dragon NOUN ajst-27745 39 26 's 's PART ajst-27745 39 27 body body NOUN ajst-27745 39 28 y y PROPN ajst-27745 39 29 ( ( PUNCT ajst-27745 39 30 m m PROPN ajst-27745 39 31 ) ) PUNCT ajst-27745 40 1 3.611935 3.611935 NUM ajst-27745 40 2 7.300518 7.300518 NUM ajst-27745 40 3 4.859957 4.859957 NUM ajst-27745 40 4 3.769426 3.769426 NUM ajst-27745 40 5 3.989175 3.989175 NUM ajst-27745 40 6 section section NOUN ajst-27745 40 7 51 51 NUM ajst-27745 40 8 of of ADP ajst-27745 40 9 the the DET ajst-27745 40 10 dragon dragon NOUN ajst-27745 40 11 's 's PART ajst-27745 40 12 body body NOUN ajst-27745 40 13 x x SYM ajst-27745 40 14 ( ( PUNCT ajst-27745 40 15 m m NOUN ajst-27745 40 16 ) ) PUNCT ajst-27745 40 17 5.169406 5.169406 NUM ajst-27745 40 18 3.536561 3.536561 NUM ajst-27745 40 19 5.813751 5.813751 NUM ajst-27745 40 20 -6.189657 -6.189657 NOUN ajst-27745 40 21 section section NOUN ajst-27745 40 22 51 51 NUM ajst-27745 40 23 of of ADP ajst-27745 40 24 the the DET ajst-27745 40 25 dragon dragon NOUN ajst-27745 40 26 's 's PART ajst-27745 40 27 body body NOUN ajst-27745 40 28 y y PROPN ajst-27745 40 29 ( ( PUNCT ajst-27745 40 30 m m PROPN ajst-27745 40 31 ) ) PUNCT ajst-27745 41 1 6.677874 6.677874 NUM ajst-27745 41 2 6.947749 6.947749 NUM ajst-27745 41 3 4.069224 4.069224 NUM ajst-27745 41 4 1.215279 1.215279 NUM ajst-27745 41 5 section section NOUN ajst-27745 41 6 101 101 NUM ajst-27745 41 7 of of ADP ajst-27745 41 8 the the DET ajst-27745 41 9 dragon dragon NOUN ajst-27745 41 10 's 's PART ajst-27745 41 11 body body NOUN ajst-27745 41 12 x x SYM ajst-27745 41 13 ( ( PUNCT ajst-27745 41 14 m m NOUN ajst-27745 41 15 ) ) PUNCT ajst-27745 41 16 1.170586 1.170586 NUM ajst-27745 41 17 5.162728 5.162728 NUM ajst-27745 41 18 -5.776372 -5.776372 NOUN ajst-27745 41 19 section section NOUN ajst-27745 41 20 101 101 NUM ajst-27745 41 21 of of ADP ajst-27745 41 22 the the DET ajst-27745 41 23 dragon dragon NOUN ajst-27745 41 24 's 's PART ajst-27745 41 25 body body NOUN ajst-27745 41 26 y y PROPN ajst-27745 41 27 ( ( PUNCT ajst-27745 41 28 m m PROPN ajst-27745 41 29 ) ) PUNCT ajst-27745 41 30 8.594989 8.594989 NUM ajst-27745 41 31 6.178448 6.178448 NUM ajst-27745 41 32 4.571165 4.571165 NUM ajst-27745 41 33 section section NOUN ajst-27745 41 34 151 151 NUM ajst-27745 41 35 of of ADP ajst-27745 41 36 the the DET ajst-27745 41 37 dragon dragon NOUN ajst-27745 41 38 's 's PART ajst-27745 41 39 body body NOUN ajst-27745 41 40 x x SYM ajst-27745 41 41 ( ( PUNCT ajst-27745 41 42 m m NOUN ajst-27745 41 43 ) ) PUNCT ajst-27745 41 44 7.427815 7.427815 NUM ajst-27745 41 45 section section NOUN ajst-27745 41 46 151 151 NUM ajst-27745 41 47 of of ADP ajst-27745 41 48 the the DET ajst-27745 41 49 dragon dragon NOUN ajst-27745 41 50 's 's PART ajst-27745 41 51 body body NOUN ajst-27745 41 52 y y PROPN ajst-27745 41 53 ( ( PUNCT ajst-27745 41 54 m m PROPN ajst-27745 41 55 ) ) PUNCT ajst-27745 41 56 3.681309 3.681309 NUM ajst-27745 41 57 section section NOUN ajst-27745 41 58 201 201 NUM ajst-27745 41 59 of of ADP ajst-27745 41 60 the the DET ajst-27745 41 61 dragon dragon NOUN ajst-27745 41 62 's 's PART ajst-27745 41 63 body body NOUN ajst-27745 41 64 x x SYM ajst-27745 41 65 ( ( PUNCT ajst-27745 41 66 m m NOUN ajst-27745 41 67 ) ) PUNCT ajst-27745 41 68 section section NOUN ajst-27745 41 69 201 201 NUM ajst-27745 41 70 of of ADP ajst-27745 41 71 the the DET ajst-27745 41 72 dragon dragon NOUN ajst-27745 41 73 's 's PART ajst-27745 41 74 body body NOUN ajst-27745 41 75 y y PROPN ajst-27745 41 76 ( ( PUNCT ajst-27745 41 77 m m NOUN ajst-27745 41 78 ) ) PUNCT ajst-27745 41 79 dragon dragon NOUN ajst-27745 41 80 's 's PART ajst-27745 41 81 tail tail NOUN ajst-27745 41 82 ( ( PUNCT ajst-27745 41 83 back back ADV ajst-27745 41 84 ) ) PUNCT ajst-27745 41 85 x x SYM ajst-27745 41 86 ( ( PUNCT ajst-27745 41 87 m m NOUN ajst-27745 41 88 ) ) PUNCT ajst-27745 41 89 dragon dragon NOUN ajst-27745 41 90 's 's PART ajst-27745 41 91 tail tail NOUN ajst-27745 41 92 ( ( PUNCT ajst-27745 41 93 back back NOUN ajst-27745 41 94 ) ) PUNCT ajst-27745 41 95 y y PROPN ajst-27745 41 96 ( ( PUNCT ajst-27745 41 97 m m PROPN ajst-27745 41 98 ) ) PUNCT ajst-27745 41 99 \ \ NOUN ajst-27745 41 100 \ \ NOUN ajst-27745 41 101 \ \ X ajst-27745 41 102 \ \ NOUN ajst-27745 41 103 Ξ» Ξ» PROPN ajst-27745 41 104 table table NOUN ajst-27745 41 105 2 2 NUM ajst-27745 41 106 . . PUNCT ajst-27745 42 1 the the DET ajst-27745 42 2 speed speed NOUN ajst-27745 42 3 of of ADP ajst-27745 42 4 the the DET ajst-27745 42 5 dragon dragon NOUN ajst-27745 42 6 dance dance NOUN ajst-27745 42 7 team team NOUN ajst-27745 42 8 at at ADP ajst-27745 42 9 each each DET ajst-27745 42 10 moment moment NOUN ajst-27745 42 11 0 0 PUNCT ajst-27745 42 12 s s PART ajst-27745 42 13 60 60 NUM ajst-27745 42 14 s s NOUN ajst-27745 42 15 120 120 NUM ajst-27745 42 16 s s NUM ajst-27745 42 17 180 180 NUM ajst-27745 42 18 s s NUM ajst-27745 42 19 240 240 NUM ajst-27745 42 20 s s NUM ajst-27745 42 21 300 300 NUM ajst-27745 42 22 s s NOUN ajst-27745 42 23 mixer mixer NOUN ajst-27745 42 24 ( ( PUNCT ajst-27745 42 25 m m PROPN ajst-27745 42 26 / / SYM ajst-27745 42 27 s s PART ajst-27745 42 28 ) ) PUNCT ajst-27745 42 29 1 1 NUM ajst-27745 42 30 1 1 NUM ajst-27745 42 31 1 1 NUM ajst-27745 42 32 1 1 NUM ajst-27745 42 33 1 1 NUM ajst-27745 42 34 1 1 NUM ajst-27745 42 35 section section NOUN ajst-27745 42 36 1 1 NUM ajst-27745 42 37 of of ADP ajst-27745 42 38 the the DET ajst-27745 42 39 dragon dragon NOUN ajst-27745 42 40 's 's PART ajst-27745 42 41 body body NOUN ajst-27745 42 42 ( ( PUNCT ajst-27745 42 43 m m NOUN ajst-27745 42 44 / / SYM ajst-27745 42 45 s s PART ajst-27745 42 46 ) ) PUNCT ajst-27745 42 47 0.999950 0.999950 NUM ajst-27745 42 48 0.999934 0.999934 NUM ajst-27745 42 49 0.999893 0.999893 NUM ajst-27745 42 50 0.999827 0.999827 NUM ajst-27745 42 51 0.999675 0.999675 NUM ajst-27745 42 52 section section NOUN ajst-27745 42 53 51 51 NUM ajst-27745 42 54 of of ADP ajst-27745 42 55 the the DET ajst-27745 42 56 dragon dragon NOUN ajst-27745 42 57 's 's PART ajst-27745 42 58 body body NOUN ajst-27745 42 59 ( ( PUNCT ajst-27745 42 60 m m NOUN ajst-27745 42 61 / / SYM ajst-27745 42 62 s s PART ajst-27745 42 63 ) ) PUNCT ajst-27745 42 64 0.999506 0.999506 NUM ajst-27745 42 65 0.999296 0.999296 NUM ajst-27745 42 66 0.998910 0.998910 NUM ajst-27745 42 67 0.998014 0.998014 NUM ajst-27745 42 68 section section NOUN ajst-27745 42 69 101 101 NUM ajst-27745 42 70 of of ADP ajst-27745 42 71 the the DET ajst-27745 42 72 dragon dragon NOUN ajst-27745 42 73 's 's PART ajst-27745 42 74 body body NOUN ajst-27745 42 75 ( ( PUNCT ajst-27745 42 76 m m NOUN ajst-27745 42 77 / / SYM ajst-27745 42 78 s s PART ajst-27745 42 79 ) ) PUNCT ajst-27745 42 80 0.998961 0.998961 NUM ajst-27745 42 81 0.998421 0.998421 NUM ajst-27745 42 82 0.997258 0.997258 NUM ajst-27745 42 83 section section NOUN ajst-27745 42 84 151 151 NUM ajst-27745 42 85 of of ADP ajst-27745 42 86 the the DET ajst-27745 42 87 dragon dragon NOUN ajst-27745 42 88 's 's PART ajst-27745 42 89 body body NOUN ajst-27745 42 90 ( ( PUNCT ajst-27745 42 91 m m NOUN ajst-27745 42 92 / / SYM ajst-27745 42 93 s s PART ajst-27745 42 94 ) ) PUNCT ajst-27745 42 95 0.996799 0.996799 NUM ajst-27745 42 96 section section NOUN ajst-27745 42 97 20 20 NUM ajst-27745 42 98 of of ADP ajst-27745 42 99 the the DET ajst-27745 42 100 dragon dragon NOUN ajst-27745 42 101 's 's PART ajst-27745 42 102 body body NOUN ajst-27745 42 103 ( ( PUNCT ajst-27745 42 104 m m NOUN ajst-27745 42 105 / / SYM ajst-27745 42 106 s s PART ajst-27745 42 107 ) ) PUNCT ajst-27745 42 108 dragon dragon NOUN ajst-27745 42 109 's 's PART ajst-27745 42 110 tail tail NOUN ajst-27745 42 111 ( ( PUNCT ajst-27745 42 112 back back NOUN ajst-27745 42 113 ) ) PUNCT ajst-27745 42 114 ( ( PUNCT ajst-27745 42 115 m m NOUN ajst-27745 42 116 / / SYM ajst-27745 42 117 s s PART ajst-27745 42 118 ) ) PUNCT ajst-27745 42 119 3 3 NUM ajst-27745 42 120 . . PUNCT ajst-27745 43 1 a a DET ajst-27745 43 2 discrete discrete ADJ ajst-27745 43 3 simulation simulation NOUN ajst-27745 43 4 - - PUNCT ajst-27745 43 5 based base VERB ajst-27745 43 6 collision collision NOUN ajst-27745 43 7 conflict conflict NOUN ajst-27745 43 8 detection detection NOUN ajst-27745 43 9 model model NOUN ajst-27745 43 10 for for ADP ajst-27745 43 11 bench bench NOUN ajst-27745 43 12 dragons dragon NOUN ajst-27745 43 13 during during ADP ajst-27745 43 14 the the DET ajst-27745 43 15 disking disking NOUN ajst-27745 43 16 - - PUNCT ajst-27745 43 17 in in ADP ajst-27745 43 18 process process NOUN ajst-27745 43 19 along along ADP ajst-27745 43 20 the the DET ajst-27745 43 21 isometric isometric ADJ ajst-27745 43 22 solenoid solenoid NOUN ajst-27745 43 23 , , PUNCT ajst-27745 43 24 the the DET ajst-27745 43 25 boarden boarden NOUN ajst-27745 43 26 dragon dragon NOUN ajst-27745 43 27 may may AUX ajst-27745 43 28 collide collide VERB ajst-27745 43 29 with with ADP ajst-27745 43 30 different different ADJ ajst-27745 43 31 sections section NOUN ajst-27745 43 32 of of ADP ajst-27745 43 33 the the DET ajst-27745 43 34 boarden boarden NOUN ajst-27745 43 35 due due ADP ajst-27745 43 36 to to ADP ajst-27745 43 37 the the DET ajst-27745 43 38 small small ADJ ajst-27745 43 39 radius radius NOUN ajst-27745 43 40 of of ADP ajst-27745 43 41 the the DET ajst-27745 43 42 dragon dragon NOUN ajst-27745 43 43 's 's PART ajst-27745 43 44 head head NOUN ajst-27745 43 45 path path NOUN ajst-27745 43 46 . . PUNCT ajst-27745 44 1 in in ADP ajst-27745 44 2 order order NOUN ajst-27745 44 3 to to PART ajst-27745 44 4 avoid avoid VERB ajst-27745 44 5 the the DET ajst-27745 44 6 collision collision NOUN ajst-27745 44 7 , , PUNCT ajst-27745 44 8 it it PRON ajst-27745 44 9 can can AUX ajst-27745 44 10 be be AUX ajst-27745 44 11 determined determine VERB ajst-27745 44 12 first first ADV ajst-27745 44 13 that that SCONJ ajst-27745 44 14 no no DET ajst-27745 44 15 collision collision NOUN ajst-27745 44 16 occurs occur VERB ajst-27745 44 17 in in ADP ajst-27745 44 18 the the DET ajst-27745 44 19 first first ADJ ajst-27745 44 20 300s 300s PROPN ajst-27745 44 21 of of ADP ajst-27745 44 22 the the DET ajst-27745 44 23 benched bench VERB ajst-27745 44 24 dragon dragon NOUN ajst-27745 44 25 , , PUNCT ajst-27745 44 26 so so SCONJ ajst-27745 44 27 this this DET ajst-27745 44 28 paper paper NOUN ajst-27745 44 29 starts start VERB ajst-27745 44 30 to to PART ajst-27745 44 31 find find VERB ajst-27745 44 32 the the DET ajst-27745 44 33 collision collision NOUN ajst-27745 44 34 point point NOUN ajst-27745 44 35 after after ADP ajst-27745 44 36 300 300 NUM ajst-27745 44 37 s. s. PROPN ajst-27745 44 38 the the DET ajst-27745 44 39 collision collision NOUN ajst-27745 44 40 detection detection NOUN ajst-27745 44 41 model model NOUN ajst-27745 44 42 is be AUX ajst-27745 44 43 developed develop VERB ajst-27745 44 44 to to PART ajst-27745 44 45 determine determine VERB ajst-27745 44 46 the the DET ajst-27745 44 47 boundary boundary ADJ ajst-27745 44 48 collision collision NOUN ajst-27745 44 49 condition condition NOUN ajst-27745 44 50 . . PUNCT ajst-27745 45 1 this this DET ajst-27745 45 2 paper paper NOUN ajst-27745 45 3 establishes establish VERB ajst-27745 45 4 a a DET ajst-27745 45 5 collision collision NOUN ajst-27745 45 6 detection detection NOUN ajst-27745 45 7 model model NOUN ajst-27745 45 8 to to PART ajst-27745 45 9 determine determine VERB ajst-27745 45 10 the the DET ajst-27745 45 11 boundary boundary ADJ ajst-27745 45 12 collision collision NOUN ajst-27745 45 13 conditions condition NOUN ajst-27745 45 14 , , PUNCT ajst-27745 45 15 and and CCONJ ajst-27745 45 16 adopts adopt VERB ajst-27745 45 17 the the DET ajst-27745 45 18 method method NOUN ajst-27745 45 19 of of ADP ajst-27745 45 20 gradually gradually ADV ajst-27745 45 21 narrowing narrow VERB ajst-27745 45 22 the the DET ajst-27745 45 23 time time NOUN ajst-27745 45 24 and and CCONJ ajst-27745 45 25 node node ADJ ajst-27745 45 26 search search NOUN ajst-27745 45 27 range range NOUN ajst-27745 45 28 in in ADP ajst-27745 45 29 the the DET ajst-27745 45 30 process process NOUN ajst-27745 45 31 of of ADP ajst-27745 45 32 solving solve VERB ajst-27745 45 33 the the DET ajst-27745 45 34 collision collision NOUN ajst-27745 45 35 moments moment NOUN ajst-27745 45 36 , , PUNCT ajst-27745 45 37 which which PRON ajst-27745 45 38 reduces reduce VERB ajst-27745 45 39 the the DET ajst-27745 45 40 time time NOUN ajst-27745 45 41 complexity complexity NOUN ajst-27745 45 42 of of ADP ajst-27745 45 43 the the DET ajst-27745 45 44 program program NOUN ajst-27745 45 45 and and CCONJ ajst-27745 45 46 improves improve VERB ajst-27745 45 47 the the DET ajst-27745 45 48 solving solving NOUN ajst-27745 45 49 accuracy accuracy NOUN ajst-27745 45 50 . . PUNCT ajst-27745 46 1 first first ADV ajst-27745 46 2 of of ADP ajst-27745 46 3 all all PRON ajst-27745 46 4 , , PUNCT ajst-27745 46 5 it it PRON ajst-27745 46 6 needs need VERB ajst-27745 46 7 to to PART ajst-27745 46 8 be be AUX ajst-27745 46 9 clear clear ADJ ajst-27745 46 10 that that SCONJ ajst-27745 46 11 the the DET ajst-27745 46 12 collision collision NOUN ajst-27745 46 13 in in ADP ajst-27745 46 14 the the DET ajst-27745 46 15 question question NOUN ajst-27745 46 16 is be AUX ajst-27745 46 17 the the DET ajst-27745 46 18 collision collision NOUN ajst-27745 46 19 between between ADP ajst-27745 46 20 the the DET ajst-27745 46 21 dragon dragon NOUN ajst-27745 46 22 head head NOUN ajst-27745 46 23 and and CCONJ ajst-27745 46 24 the the DET ajst-27745 46 25 dragon dragon NOUN ajst-27745 46 26 body body NOUN ajst-27745 46 27 , , PUNCT ajst-27745 46 28 and and CCONJ ajst-27745 46 29 it it PRON ajst-27745 46 30 occurs occur VERB ajst-27745 46 31 in in ADP ajst-27745 46 32 the the DET ajst-27745 46 33 inner inner ADJ ajst-27745 46 34 circle circle NOUN ajst-27745 46 35 . . PUNCT ajst-27745 47 1 because because SCONJ ajst-27745 47 2 the the DET ajst-27745 47 3 radius radius NOUN ajst-27745 47 4 is be AUX ajst-27745 47 5 smaller small ADJ ajst-27745 47 6 in in ADP ajst-27745 47 7 the the DET ajst-27745 47 8 inner inner ADJ ajst-27745 47 9 circle circle NOUN ajst-27745 47 10 , , PUNCT ajst-27745 47 11 the the DET ajst-27745 47 12 arc arc NOUN ajst-27745 47 13 of of ADP ajst-27745 47 14 the the DET ajst-27745 47 15 dragon dragon NOUN ajst-27745 47 16 head head NOUN ajst-27745 47 17 under under ADP ajst-27745 47 18 the the DET ajst-27745 47 19 same same ADJ ajst-27745 47 20 length length NOUN ajst-27745 47 21 ( ( PUNCT ajst-27745 47 22 chord chord NOUN ajst-27745 47 23 length length NOUN ajst-27745 47 24 ) ) PUNCT ajst-27745 47 25 is be AUX ajst-27745 47 26 larger large ADJ ajst-27745 47 27 , , PUNCT ajst-27745 47 28 the the DET ajst-27745 47 29 angle angle NOUN ajst-27745 47 30 across across ADP ajst-27745 47 31 is be AUX ajst-27745 47 32 larger large ADJ ajst-27745 47 33 , , PUNCT ajst-27745 47 34 and and CCONJ ajst-27745 47 35 it it PRON ajst-27745 47 36 is be AUX ajst-27745 47 37 more more ADV ajst-27745 47 38 likely likely ADJ ajst-27745 47 39 to to PART ajst-27745 47 40 collide collide VERB ajst-27745 47 41 with with ADP ajst-27745 47 42 the the DET ajst-27745 47 43 dragon dragon NOUN ajst-27745 47 44 body body NOUN ajst-27745 47 45 segments segment NOUN ajst-27745 47 46 , , PUNCT ajst-27745 47 47 and and CCONJ ajst-27745 47 48 the the DET ajst-27745 47 49 schematic schematic ADJ ajst-27745 47 50 diagram diagram NOUN ajst-27745 47 51 of of ADP ajst-27745 47 52 the the DET ajst-27745 47 53 collision collision NOUN ajst-27745 47 54 nodes node NOUN ajst-27745 47 55 is be AUX ajst-27745 47 56 given give VERB ajst-27745 47 57 in in ADP ajst-27745 47 58 figure figure NOUN ajst-27745 47 59 3 3 NUM ajst-27745 47 60 below below ADV ajst-27745 47 61 . . PUNCT ajst-27745 48 1 300 300 NUM ajst-27745 48 2 figure figure NOUN ajst-27745 48 3 3 3 NUM ajst-27745 48 4 . . PUNCT ajst-27745 48 5 schematic schematic ADJ ajst-27745 48 6 diagram diagram NOUN ajst-27745 48 7 of of ADP ajst-27745 48 8 collision collision NOUN ajst-27745 48 9 nodes node NOUN ajst-27745 48 10 as as SCONJ ajst-27745 48 11 can can AUX ajst-27745 48 12 be be AUX ajst-27745 48 13 seen see VERB ajst-27745 48 14 from from ADP ajst-27745 48 15 the the DET ajst-27745 48 16 figure figure NOUN ajst-27745 48 17 , , PUNCT ajst-27745 48 18 on on ADP ajst-27745 48 19 the the DET ajst-27745 48 20 inside inside NOUN ajst-27745 48 21 of of ADP ajst-27745 48 22 the the DET ajst-27745 48 23 coil coil NOUN ajst-27745 48 24 , , PUNCT ajst-27745 48 25 the the DET ajst-27745 48 26 curvature curvature NOUN ajst-27745 48 27 of of ADP ajst-27745 48 28 the the DET ajst-27745 48 29 arc arc NOUN ajst-27745 48 30 is be AUX ajst-27745 48 31 large large ADJ ajst-27745 48 32 , , PUNCT ajst-27745 48 33 the the DET ajst-27745 48 34 red red ADJ ajst-27745 48 35 dragon dragon NOUN ajst-27745 48 36 swings swing NOUN ajst-27745 48 37 through through ADP ajst-27745 48 38 a a DET ajst-27745 48 39 large large ADJ ajst-27745 48 40 angle angle NOUN ajst-27745 48 41 , , PUNCT ajst-27745 48 42 and and CCONJ ajst-27745 48 43 is be AUX ajst-27745 48 44 more more ADV ajst-27745 48 45 likely likely ADJ ajst-27745 48 46 to to PART ajst-27745 48 47 collide collide VERB ajst-27745 48 48 with with ADP ajst-27745 48 49 the the DET ajst-27745 48 50 blue blue ADJ ajst-27745 48 51 dragon dragon NOUN ajst-27745 48 52 body body NOUN ajst-27745 48 53 . . PUNCT ajst-27745 49 1 on on ADP ajst-27745 49 2 the the DET ajst-27745 49 3 other other ADJ ajst-27745 49 4 hand hand NOUN ajst-27745 49 5 , , PUNCT ajst-27745 49 6 on on ADP ajst-27745 49 7 the the DET ajst-27745 49 8 outside outside NOUN ajst-27745 49 9 of of ADP ajst-27745 49 10 the the DET ajst-27745 49 11 coil coil NOUN ajst-27745 49 12 , , PUNCT ajst-27745 49 13 the the DET ajst-27745 49 14 curvature curvature NOUN ajst-27745 49 15 of of ADP ajst-27745 49 16 the the DET ajst-27745 49 17 arc arc NOUN ajst-27745 49 18 is be AUX ajst-27745 49 19 small small ADJ ajst-27745 49 20 , , PUNCT ajst-27745 49 21 and and CCONJ ajst-27745 49 22 the the DET ajst-27745 49 23 angle angle NOUN ajst-27745 49 24 of of ADP ajst-27745 49 25 rotation rotation NOUN ajst-27745 49 26 of of ADP ajst-27745 49 27 the the DET ajst-27745 49 28 dragon dragon NOUN ajst-27745 49 29 's 's PART ajst-27745 49 30 body body NOUN ajst-27745 49 31 is be AUX ajst-27745 49 32 small small ADJ ajst-27745 49 33 , , PUNCT ajst-27745 49 34 so so SCONJ ajst-27745 49 35 there there PRON ajst-27745 49 36 will will AUX ajst-27745 49 37 be be AUX ajst-27745 49 38 no no DET ajst-27745 49 39 collision collision NOUN ajst-27745 49 40 . . PUNCT ajst-27745 50 1 secondly secondly ADV ajst-27745 50 2 , , PUNCT ajst-27745 50 3 the the DET ajst-27745 50 4 collision collision NOUN ajst-27745 50 5 can can AUX ajst-27745 50 6 not not PART ajst-27745 50 7 be be AUX ajst-27745 50 8 an an DET ajst-27745 50 9 edge edge NOUN ajst-27745 50 10 - - PUNCT ajst-27745 50 11 to to ADP ajst-27745 50 12 - - PUNCT ajst-27745 50 13 edge edge NOUN ajst-27745 50 14 collision collision NOUN ajst-27745 50 15 , , PUNCT ajst-27745 50 16 but but CCONJ ajst-27745 50 17 a a DET ajst-27745 50 18 top top ADJ ajst-27745 50 19 corner corner NOUN ajst-27745 50 20 - - PUNCT ajst-27745 50 21 to to ADP ajst-27745 50 22 - - PUNCT ajst-27745 50 23 edge edge NOUN ajst-27745 50 24 collision collision NOUN ajst-27745 50 25 . . PUNCT ajst-27745 51 1 because because SCONJ ajst-27745 51 2 the the DET ajst-27745 51 3 two two NUM ajst-27745 51 4 handles handle NOUN ajst-27745 51 5 are be AUX ajst-27745 51 6 located locate VERB ajst-27745 51 7 on on ADP ajst-27745 51 8 the the DET ajst-27745 51 9 same same ADJ ajst-27745 51 10 thread thread NOUN ajst-27745 51 11 , , PUNCT ajst-27745 51 12 the the DET ajst-27745 51 13 distance distance NOUN ajst-27745 51 14 between between ADP ajst-27745 51 15 the the DET ajst-27745 51 16 two two NUM ajst-27745 51 17 threads thread NOUN ajst-27745 51 18 is be AUX ajst-27745 51 19 55 55 NUM ajst-27745 51 20 cm cm NOUN ajst-27745 51 21 , , PUNCT ajst-27745 51 22 and and CCONJ ajst-27745 51 23 the the DET ajst-27745 51 24 distance distance NOUN ajst-27745 51 25 between between ADP ajst-27745 51 26 the the DET ajst-27745 51 27 center center ADJ ajst-27745 51 28 axes axis NOUN ajst-27745 51 29 of of ADP ajst-27745 51 30 the the DET ajst-27745 51 31 board board NOUN ajst-27745 51 32 is be AUX ajst-27745 51 33 2 2 NUM ajst-27745 51 34 βˆ— βˆ— NOUN ajst-27745 51 35 15 15 NUM ajst-27745 51 36 30 30 NUM ajst-27745 51 37 cm cm NOUN ajst-27745 51 38 , , PUNCT ajst-27745 51 39 which which PRON ajst-27745 51 40 is be AUX ajst-27745 51 41 smaller small ADJ ajst-27745 51 42 than than ADP ajst-27745 51 43 the the DET ajst-27745 51 44 distance distance NOUN ajst-27745 51 45 between between ADP ajst-27745 51 46 the the DET ajst-27745 51 47 threads thread NOUN ajst-27745 51 48 , , PUNCT ajst-27745 51 49 so so SCONJ ajst-27745 51 50 it it PRON ajst-27745 51 51 is be AUX ajst-27745 51 52 impossible impossible ADJ ajst-27745 51 53 for for SCONJ ajst-27745 51 54 the the DET ajst-27745 51 55 board board NOUN ajst-27745 51 56 to to PART ajst-27745 51 57 have have VERB ajst-27745 51 58 an an DET ajst-27745 51 59 edgeto edgeto ADJ ajst-27745 51 60 - - PUNCT ajst-27745 51 61 edge edge NOUN ajst-27745 51 62 collision collision NOUN ajst-27745 51 63 . . PUNCT ajst-27745 52 1 we we PRON ajst-27745 52 2 start start VERB ajst-27745 52 3 looking look VERB ajst-27745 52 4 for for ADP ajst-27745 52 5 the the DET ajst-27745 52 6 collision collision NOUN ajst-27745 52 7 point point NOUN ajst-27745 52 8 after after ADP ajst-27745 52 9 300 300 NUM ajst-27745 52 10 s. s. PROPN ajst-27745 52 11 the the DET ajst-27745 52 12 first first ADJ ajst-27745 52 13 step step NOUN ajst-27745 52 14 is be AUX ajst-27745 52 15 to to PART ajst-27745 52 16 determine determine VERB ajst-27745 52 17 the the DET ajst-27745 52 18 location location NOUN ajst-27745 52 19 of of ADP ajst-27745 52 20 the the DET ajst-27745 52 21 faucet faucet NOUN ajst-27745 52 22 . . PUNCT ajst-27745 53 1 first first ADV ajst-27745 53 2 , , PUNCT ajst-27745 53 3 we we PRON ajst-27745 53 4 determine determine VERB ajst-27745 53 5 the the DET ajst-27745 53 6 location location NOUN ajst-27745 53 7 of of ADP ajst-27745 53 8 the the DET ajst-27745 53 9 faucet faucet NOUN ajst-27745 53 10 . . PUNCT ajst-27745 54 1 according accord VERB ajst-27745 54 2 to to ADP ajst-27745 54 3 the the DET ajst-27745 54 4 model model NOUN ajst-27745 54 5 established establish VERB ajst-27745 54 6 in in ADP ajst-27745 54 7 the the DET ajst-27745 54 8 previous previous ADJ ajst-27745 54 9 chapter chapter NOUN ajst-27745 54 10 , , PUNCT ajst-27745 54 11 the the DET ajst-27745 54 12 location location NOUN ajst-27745 54 13 of of ADP ajst-27745 54 14 the the DET ajst-27745 54 15 faucet faucet NOUN ajst-27745 54 16 corresponds correspond VERB ajst-27745 54 17 to to ADP ajst-27745 54 18 the the DET ajst-27745 54 19 time time NOUN ajst-27745 54 20 , , PUNCT ajst-27745 54 21 so so CCONJ ajst-27745 54 22 the the DET ajst-27745 54 23 termination termination NOUN ajst-27745 54 24 moment moment NOUN ajst-27745 54 25 of of ADP ajst-27745 54 26 the the DET ajst-27745 54 27 disk disk NOUN ajst-27745 54 28 - - PUNCT ajst-27745 54 29 in in NOUN ajst-27745 54 30 can can AUX ajst-27745 54 31 be be AUX ajst-27745 54 32 determined determine VERB ajst-27745 54 33 by by ADP ajst-27745 54 34 the the DET ajst-27745 54 35 location location NOUN ajst-27745 54 36 of of ADP ajst-27745 54 37 the the DET ajst-27745 54 38 faucet faucet PROPN ajst-27745 54 39 collision collision NOUN ajst-27745 54 40 . . PUNCT ajst-27745 55 1 discretize discretize VERB ajst-27745 55 2 the the DET ajst-27745 55 3 trajectory trajectory NOUN ajst-27745 55 4 of of ADP ajst-27745 55 5 the the DET ajst-27745 55 6 dragon dragon NOUN ajst-27745 55 7 head head NOUN ajst-27745 55 8 after after ADP ajst-27745 55 9 300s 300s PROPN ajst-27745 55 10 , , PUNCT ajst-27745 55 11 and and CCONJ ajst-27745 55 12 gradually gradually ADV ajst-27745 55 13 increase increase VERB ajst-27745 55 14 the the DET ajst-27745 55 15 degree degree NOUN ajst-27745 55 16 of of ADP ajst-27745 55 17 discretization discretization NOUN ajst-27745 55 18 of of ADP ajst-27745 55 19 the the DET ajst-27745 55 20 inner inner ADJ ajst-27745 55 21 circle circle NOUN ajst-27745 55 22 . . PUNCT ajst-27745 56 1 the the DET ajst-27745 56 2 angle angle NOUN ajst-27745 56 3 of of ADP ajst-27745 56 4 the the DET ajst-27745 56 5 inner inner ADJ ajst-27745 56 6 circle circle NOUN ajst-27745 56 7 is be AUX ajst-27745 56 8 uniformly uniformly ADV ajst-27745 56 9 discretized discretize VERB ajst-27745 56 10 into into ADP ajst-27745 56 11 1000 1000 NUM ajst-27745 56 12 copies copy NOUN ajst-27745 56 13 , , PUNCT ajst-27745 56 14 and and CCONJ ajst-27745 56 15 the the DET ajst-27745 56 16 front front ADJ ajst-27745 56 17 handles handle NOUN ajst-27745 56 18 of of ADP ajst-27745 56 19 the the DET ajst-27745 56 20 faucet faucet NOUN ajst-27745 56 21 are be AUX ajst-27745 56 22 placed place VERB ajst-27745 56 23 at at ADP ajst-27745 56 24 the the DET ajst-27745 56 25 discretized discretized ADJ ajst-27745 56 26 points point NOUN ajst-27745 56 27 in in ADP ajst-27745 56 28 turn turn NOUN ajst-27745 56 29 , , PUNCT ajst-27745 56 30 so so SCONJ ajst-27745 56 31 that that SCONJ ajst-27745 56 32 the the DET ajst-27745 56 33 geometric geometric ADJ ajst-27745 56 34 positions position NOUN ajst-27745 56 35 of of ADP ajst-27745 56 36 the the DET ajst-27745 56 37 faucet faucet NOUN ajst-27745 56 38 and and CCONJ ajst-27745 56 39 the the DET ajst-27745 56 40 dragon dragon NOUN ajst-27745 56 41 body body NOUN ajst-27745 56 42 are be AUX ajst-27745 56 43 determined determine VERB ajst-27745 56 44 , , PUNCT ajst-27745 56 45 and and CCONJ ajst-27745 56 46 then then ADV ajst-27745 56 47 the the DET ajst-27745 56 48 collision collision NOUN ajst-27745 56 49 detection detection NOUN ajst-27745 56 50 is be AUX ajst-27745 56 51 carried carry VERB ajst-27745 56 52 out out ADP ajst-27745 56 53 . . PUNCT ajst-27745 57 1 let let VERB ajst-27745 57 2 the the DET ajst-27745 57 3 positions position NOUN ajst-27745 57 4 of of ADP ajst-27745 57 5 the the DET ajst-27745 57 6 two two NUM ajst-27745 57 7 handles handle NOUN ajst-27745 57 8 be be VERB ajst-27745 57 9 π‘₯1 π‘₯1 NOUN ajst-27745 57 10 , , PUNCT ajst-27745 57 11 𝑦1 𝑦1 NOUN ajst-27745 57 12 , , PUNCT ajst-27745 57 13 π‘₯2 π‘₯2 NOUN ajst-27745 57 14 , , PUNCT ajst-27745 57 15 𝑦2 𝑦2 NOUN ajst-27745 57 16 respectively respectively ADV ajst-27745 57 17 , , PUNCT ajst-27745 57 18 and and CCONJ ajst-27745 57 19 the the DET ajst-27745 57 20 two two NUM ajst-27745 57 21 auxiliary auxiliary ADJ ajst-27745 57 22 direction direction NOUN ajst-27745 57 23 vectors vector NOUN ajst-27745 57 24 are be AUX ajst-27745 57 25 οΏ½ οΏ½ NOUN ajst-27745 57 26 βƒ— βƒ— NOUN ajst-27745 57 27 οΏ½ οΏ½ NOUN ajst-27745 57 28 1 1 NUM ajst-27745 57 29 , , PUNCT ajst-27745 57 30 οΏ½ οΏ½ PROPN ajst-27745 57 31 βƒ— βƒ— NOUN ajst-27745 57 32 οΏ½ οΏ½ NOUN ajst-27745 57 33 2 2 NUM ajst-27745 57 34 as as SCONJ ajst-27745 57 35 shown show VERB ajst-27745 57 36 in in ADP ajst-27745 57 37 the the DET ajst-27745 57 38 figure figure NOUN ajst-27745 57 39 , , PUNCT ajst-27745 57 40 and and CCONJ ajst-27745 57 41 we we PRON ajst-27745 57 42 utilize utilize VERB ajst-27745 57 43 the the DET ajst-27745 57 44 property property NOUN ajst-27745 57 45 of of ADP ajst-27745 57 46 vector vector NOUN ajst-27745 57 47 addition addition NOUN ajst-27745 57 48 and and CCONJ ajst-27745 57 49 subtraction subtraction NOUN ajst-27745 57 50 to to PART ajst-27745 57 51 solve solve VERB ajst-27745 57 52 for for ADP ajst-27745 57 53 the the DET ajst-27745 57 54 position position NOUN ajst-27745 57 55 of of ADP ajst-27745 57 56 the the DET ajst-27745 57 57 top top ADJ ajst-27745 57 58 angle angle NOUN ajst-27745 57 59 , , PUNCT ajst-27745 57 60 which which PRON ajst-27745 57 61 is be AUX ajst-27745 57 62 derived derive VERB ajst-27745 57 63 as as SCONJ ajst-27745 57 64 follows follow VERB ajst-27745 57 65 : : PUNCT ajst-27745 57 66 the the DET ajst-27745 57 67 two two NUM ajst-27745 57 68 handles handle NOUN ajst-27745 57 69 form form VERB ajst-27745 57 70 a a DET ajst-27745 57 71 vector vector NOUN ajst-27745 57 72 οΏ½ οΏ½ NOUN ajst-27745 57 73 βƒ— βƒ— NOUN ajst-27745 57 74 οΏ½ οΏ½ ADP ajst-27745 57 75 π‘₯ π‘₯ ADP ajst-27745 57 76 π‘₯ π‘₯ X ajst-27745 57 77 , , PUNCT ajst-27745 57 78 𝑦 𝑦 PRON ajst-27745 57 79 𝑦 𝑦 NOUN ajst-27745 57 80 and and CCONJ ajst-27745 57 81 the the DET ajst-27745 57 82 unit unit NOUN ajst-27745 57 83 vector vector NOUN ajst-27745 57 84 in in ADP ajst-27745 57 85 that that DET ajst-27745 57 86 direction direction NOUN ajst-27745 57 87 is be AUX ajst-27745 57 88 given give VERB ajst-27745 57 89 in in ADP ajst-27745 57 90 the the DET ajst-27745 57 91 following follow VERB ajst-27745 57 92 equation equation NOUN ajst-27745 57 93 : : PUNCT ajst-27745 57 94 𝑒 𝑒 X ajst-27745 57 95 , , PUNCT ajst-27745 57 96 ( ( PUNCT ajst-27745 57 97 14 14 NUM ajst-27745 57 98 ) ) PUNCT ajst-27745 57 99 similarly similarly ADV ajst-27745 57 100 , , PUNCT ajst-27745 57 101 the the DET ajst-27745 57 102 unit unit NOUN ajst-27745 57 103 vector vector NOUN ajst-27745 57 104 perpendicular perpendicular NOUN ajst-27745 57 105 to to ADP ajst-27745 57 106 it it PRON ajst-27745 57 107 is be AUX ajst-27745 57 108 given give VERB ajst-27745 57 109 by by ADP ajst-27745 57 110 the the DET ajst-27745 57 111 following follow VERB ajst-27745 57 112 equation equation NOUN ajst-27745 57 113 : : PUNCT ajst-27745 57 114 𝑒 𝑒 X ajst-27745 57 115 , , PUNCT ajst-27745 57 116 ( ( PUNCT ajst-27745 57 117 15 15 NUM ajst-27745 57 118 ) ) PUNCT ajst-27745 57 119 the the DET ajst-27745 57 120 distance distance NOUN ajst-27745 57 121 of of ADP ajst-27745 57 122 the the DET ajst-27745 57 123 handle handle NOUN ajst-27745 57 124 from from ADP ajst-27745 57 125 the the DET ajst-27745 57 126 front front NOUN ajst-27745 57 127 of of ADP ajst-27745 57 128 the the DET ajst-27745 57 129 dragon dragon NOUN ajst-27745 57 130 is be AUX ajst-27745 57 131 27.5 27.5 NUM ajst-27745 57 132 cm cm NOUN ajst-27745 57 133 , , PUNCT ajst-27745 57 134 and and CCONJ ajst-27745 57 135 the the DET ajst-27745 57 136 direction direction NOUN ajst-27745 57 137 is be AUX ajst-27745 57 138 𝑒 𝑒 ADJ ajst-27745 57 139 ; ; PUNCT ajst-27745 57 140 half half NOUN ajst-27745 57 141 of of ADP ajst-27745 57 142 the the DET ajst-27745 57 143 width width NOUN ajst-27745 57 144 of of ADP ajst-27745 57 145 the the DET ajst-27745 57 146 boarder boarder NOUN ajst-27745 57 147 is be AUX ajst-27745 57 148 15 15 NUM ajst-27745 57 149 cm cm NOUN ajst-27745 57 150 , , PUNCT ajst-27745 57 151 and and CCONJ ajst-27745 57 152 the the DET ajst-27745 57 153 direction direction NOUN ajst-27745 57 154 is be AUX ajst-27745 57 155 𝑒 𝑒 ADP ajst-27745 57 156 , , PUNCT ajst-27745 57 157 so so SCONJ ajst-27745 57 158 we we PRON ajst-27745 57 159 can can AUX ajst-27745 57 160 get get VERB ajst-27745 57 161 the the DET ajst-27745 57 162 vector vector NOUN ajst-27745 57 163 𝑏 𝑏 PROPN ajst-27745 57 164 of of ADP ajst-27745 57 165 the the DET ajst-27745 57 166 top top ADJ ajst-27745 57 167 angle angle NOUN ajst-27745 57 168 as as SCONJ ajst-27745 57 169 follows follow VERB ajst-27745 57 170 : : PUNCT ajst-27745 57 171 𝑏 𝑏 PRON ajst-27745 57 172 οΏ½ οΏ½ PROPN ajst-27745 57 173 βƒ— βƒ— NOUN ajst-27745 57 174 οΏ½ οΏ½ PROPN ajst-27745 57 175 27.5𝑒 27.5𝑒 NUM ajst-27745 57 176 15𝑒 15𝑒 NOUN ajst-27745 57 177 ( ( PUNCT ajst-27745 57 178 16 16 NUM ajst-27745 57 179 ) ) PUNCT ajst-27745 57 180 after after ADP ajst-27745 57 181 obtaining obtain VERB ajst-27745 57 182 the the DET ajst-27745 57 183 coordinates coordinate NOUN ajst-27745 57 184 of of ADP ajst-27745 57 185 the the DET ajst-27745 57 186 top top ADJ ajst-27745 57 187 corners corner NOUN ajst-27745 57 188 , , PUNCT ajst-27745 57 189 it it PRON ajst-27745 57 190 is be AUX ajst-27745 57 191 sufficient sufficient ADJ ajst-27745 57 192 to to PART ajst-27745 57 193 use use VERB ajst-27745 57 194 the the DET ajst-27745 57 195 four four NUM ajst-27745 57 196 top top ADJ ajst-27745 57 197 corners corner NOUN ajst-27745 57 198 of of ADP ajst-27745 57 199 the the DET ajst-27745 57 200 dragon dragon NOUN ajst-27745 57 201 head head NOUN ajst-27745 57 202 to to PART ajst-27745 57 203 detect detect VERB ajst-27745 57 204 the the DET ajst-27745 57 205 collision collision NOUN ajst-27745 57 206 with with ADP ajst-27745 57 207 the the DET ajst-27745 57 208 dragon dragon NOUN ajst-27745 57 209 body body NOUN ajst-27745 57 210 of of ADP ajst-27745 57 211 the the DET ajst-27745 57 212 innermost innermost ADJ ajst-27745 57 213 and and CCONJ ajst-27745 57 214 penultimate penultimate NOUN ajst-27745 57 215 circles circle NOUN ajst-27745 57 216 without without ADP ajst-27745 57 217 using use VERB ajst-27745 57 218 the the DET ajst-27745 57 219 outer outer ADJ ajst-27745 57 220 dragon dragon NOUN ajst-27745 57 221 body body NOUN ajst-27745 57 222 for for ADP ajst-27745 57 223 detection detection NOUN ajst-27745 57 224 . . PUNCT ajst-27745 58 1 since since SCONJ ajst-27745 58 2 the the DET ajst-27745 58 3 innermost innermost NOUN ajst-27745 58 4 and and CCONJ ajst-27745 58 5 penultimate penultimate NOUN ajst-27745 58 6 circles circle NOUN ajst-27745 58 7 have have VERB ajst-27745 58 8 more more ADJ ajst-27745 58 9 loci locus NOUN ajst-27745 58 10 after after ADP ajst-27745 58 11 discretization discretization NOUN ajst-27745 58 12 and and CCONJ ajst-27745 58 13 it it PRON ajst-27745 58 14 takes take VERB ajst-27745 58 15 longer long ADJ ajst-27745 58 16 computation computation NOUN ajst-27745 58 17 time time NOUN ajst-27745 58 18 to to PART ajst-27745 58 19 detect detect VERB ajst-27745 58 20 the the DET ajst-27745 58 21 collision collision NOUN ajst-27745 58 22 one one NUM ajst-27745 58 23 by by ADP ajst-27745 58 24 one one NUM ajst-27745 58 25 , , PUNCT ajst-27745 58 26 we we PRON ajst-27745 58 27 do do VERB ajst-27745 58 28 a a DET ajst-27745 58 29 round round NOUN ajst-27745 58 30 of of ADP ajst-27745 58 31 screening screen VERB ajst-27745 58 32 first first ADV ajst-27745 58 33 , , PUNCT ajst-27745 58 34 taking take VERB ajst-27745 58 35 the the DET ajst-27745 58 36 distance distance NOUN ajst-27745 58 37 𝑠𝑖𝑗 𝑠𝑖𝑗 NOUN ajst-27745 58 38 from from ADP ajst-27745 58 39 the the DET ajst-27745 58 40 𝑖-th 𝑖-th PROPN ajst-27745 58 41 vertex vertex NOUN ajst-27745 58 42 corner corner NOUN ajst-27745 58 43 of of ADP ajst-27745 58 44 the the DET ajst-27745 58 45 dragon dragon NOUN ajst-27745 58 46 's 's PART ajst-27745 58 47 headboard headboard NOUN ajst-27745 58 48 to to ADP ajst-27745 58 49 the the DET ajst-27745 58 50 side side NOUN ajst-27745 58 51 of of ADP ajst-27745 58 52 the the DET ajst-27745 58 53 𝑗-th 𝑗-th NOUN ajst-27745 58 54 boardboard boardboard NOUN ajst-27745 58 55 as as ADP ajst-27745 58 56 the the DET ajst-27745 58 57 basket basket NOUN ajst-27745 58 58 selection selection NOUN ajst-27745 58 59 criterion criterion NOUN ajst-27745 58 60 , , PUNCT ajst-27745 58 61 and and CCONJ ajst-27745 58 62 set set VERB ajst-27745 58 63 a a DET ajst-27745 58 64 smaller small ADJ ajst-27745 58 65 threshold threshold NOUN ajst-27745 58 66 m m PROPN ajst-27745 58 67 , , PUNCT ajst-27745 58 68 and and CCONJ ajst-27745 58 69 perform perform VERB ajst-27745 58 70 the the DET ajst-27745 58 71 second second ADJ ajst-27745 58 72 round round NOUN ajst-27745 58 73 of of ADP ajst-27745 58 74 collision collision NOUN ajst-27745 58 75 modeling model VERB ajst-27745 58 76 only only ADV ajst-27745 58 77 when when SCONJ ajst-27745 58 78 𝑠𝑖𝑗 𝑠𝑖𝑗 PROPN ajst-27745 58 79 π‘š. π‘š. PROPN ajst-27745 58 80 𝑠𝑖𝑗 𝑠𝑖𝑗 PROPN ajst-27745 58 81 is be AUX ajst-27745 58 82 given give VERB ajst-27745 58 83 by by ADP ajst-27745 58 84 the the DET ajst-27745 58 85 equation equation NOUN ajst-27745 58 86 of of ADP ajst-27745 58 87 the the DET ajst-27745 58 88 distance distance NOUN ajst-27745 58 89 from from ADP ajst-27745 58 90 a a DET ajst-27745 58 91 point point NOUN ajst-27745 58 92 to to ADP ajst-27745 58 93 a a DET ajst-27745 58 94 straight straight ADJ ajst-27745 58 95 line line NOUN ajst-27745 58 96 , , PUNCT ajst-27745 58 97 which which PRON ajst-27745 58 98 passes pass VERB ajst-27745 58 99 through through ADP ajst-27745 58 100 the the DET ajst-27745 58 101 top top ADJ ajst-27745 58 102 corner corner NOUN ajst-27745 58 103 π‘₯ π‘₯ PROPN ajst-27745 58 104 , , PUNCT ajst-27745 58 105 𝑦 𝑦 NOUN ajst-27745 58 106 , , PUNCT ajst-27745 58 107 π‘₯ π‘₯ X ajst-27745 58 108 , , PUNCT ajst-27745 58 109 𝑦 𝑦 NOUN ajst-27745 58 110 points point NOUN ajst-27745 58 111 , , PUNCT ajst-27745 58 112 then then ADV ajst-27745 58 113 the the DET ajst-27745 58 114 equation equation NOUN ajst-27745 58 115 of of ADP ajst-27745 58 116 the the DET ajst-27745 58 117 straight straight ADJ ajst-27745 58 118 line line NOUN ajst-27745 58 119 can can AUX ajst-27745 58 120 be be AUX ajst-27745 58 121 expressed express VERB ajst-27745 58 122 in in ADP ajst-27745 58 123 the the DET ajst-27745 58 124 coordinates coordinate NOUN ajst-27745 58 125 of of ADP ajst-27745 58 126 the the DET ajst-27745 58 127 two two NUM ajst-27745 58 128 points point NOUN ajst-27745 58 129 . . PUNCT ajst-27745 59 1 let let VERB ajst-27745 59 2 the the DET ajst-27745 59 3 equation equation NOUN ajst-27745 59 4 of of ADP ajst-27745 59 5 the the DET ajst-27745 59 6 line line NOUN ajst-27745 59 7 for for ADP ajst-27745 59 8 𝑦 𝑦 NUM ajst-27745 59 9 π‘˜π‘₯ π‘˜π‘₯ NOUN ajst-27745 59 10 𝑏 𝑏 NOUN ajst-27745 59 11 , , PUNCT ajst-27745 59 12 the the DET ajst-27745 59 13 coordinates coordinate NOUN ajst-27745 59 14 of of ADP ajst-27745 59 15 the the DET ajst-27745 59 16 top top ADJ ajst-27745 59 17 corner corner NOUN ajst-27745 59 18 of of ADP ajst-27745 59 19 π‘₯ π‘₯ PRON ajst-27745 59 20 , , PUNCT ajst-27745 59 21 𝑦 𝑦 NOUN ajst-27745 59 22 , , PUNCT ajst-27745 59 23 then then ADV ajst-27745 60 1 𝑠 𝑠 INTJ ajst-27745 61 1 | | ADV ajst-27745 62 1 | | INTJ ajst-27745 62 2 ( ( PUNCT ajst-27745 62 3 17 17 NUM ajst-27745 62 4 ) ) PUNCT ajst-27745 62 5 in in ADP ajst-27745 62 6 this this DET ajst-27745 62 7 paper paper NOUN ajst-27745 62 8 , , PUNCT ajst-27745 62 9 a a DET ajst-27745 62 10 geometric geometric ADJ ajst-27745 62 11 method method NOUN ajst-27745 62 12 is be AUX ajst-27745 62 13 used use VERB ajst-27745 62 14 to to PART ajst-27745 62 15 construct construct VERB ajst-27745 62 16 a a DET ajst-27745 62 17 collision collision NOUN ajst-27745 62 18 conflict conflict NOUN ajst-27745 62 19 detection detection NOUN ajst-27745 62 20 model model NOUN ajst-27745 62 21 . . PUNCT ajst-27745 63 1 for for ADP ajst-27745 63 2 any any DET ajst-27745 63 3 point point NOUN ajst-27745 63 4 in in ADP ajst-27745 63 5 the the DET ajst-27745 63 6 plane plane NOUN ajst-27745 63 7 of of ADP ajst-27745 63 8 the the DET ajst-27745 63 9 dragon dragon NOUN ajst-27745 63 10 body body NOUN ajst-27745 63 11 boarding boarding NOUN ajst-27745 63 12 , , PUNCT ajst-27745 63 13 respectively respectively ADV ajst-27745 63 14 , , PUNCT ajst-27745 63 15 connecting connect VERB ajst-27745 63 16 its its PRON ajst-27745 63 17 four four NUM ajst-27745 63 18 vertices vertex NOUN ajst-27745 63 19 with with ADP ajst-27745 63 20 the the DET ajst-27745 63 21 dragon dragon NOUN ajst-27745 63 22 body body NOUN ajst-27745 63 23 boarding boarding NOUN ajst-27745 63 24 , , PUNCT ajst-27745 63 25 constituting constitute VERB ajst-27745 63 26 four four NUM ajst-27745 63 27 triangles triangle NOUN ajst-27745 63 28 , , PUNCT ajst-27745 63 29 if if SCONJ ajst-27745 63 30 the the DET ajst-27745 63 31 sum sum NOUN ajst-27745 63 32 of of ADP ajst-27745 63 33 the the DET ajst-27745 63 34 area area NOUN ajst-27745 63 35 of of ADP ajst-27745 63 36 these these DET ajst-27745 63 37 four four NUM ajst-27745 63 38 triangles triangle NOUN ajst-27745 63 39 is be AUX ajst-27745 63 40 equal equal ADJ ajst-27745 63 41 to to ADP ajst-27745 63 42 the the DET ajst-27745 63 43 boarding boarding NOUN ajst-27745 63 44 rectangle rectangle NOUN ajst-27745 63 45 area area NOUN ajst-27745 63 46 , , PUNCT ajst-27745 63 47 the the DET ajst-27745 63 48 point point NOUN ajst-27745 63 49 is be AUX ajst-27745 63 50 located locate VERB ajst-27745 63 51 in in ADP ajst-27745 63 52 the the DET ajst-27745 63 53 boarding boarding NOUN ajst-27745 63 54 rectangle rectangle NOUN ajst-27745 63 55 , , PUNCT ajst-27745 63 56 that that ADV ajst-27745 63 57 is is ADV ajst-27745 63 58 , , PUNCT ajst-27745 63 59 the the DET ajst-27745 63 60 collision collision NOUN ajst-27745 63 61 occurs occur VERB ajst-27745 63 62 ; ; PUNCT ajst-27745 63 63 if if SCONJ ajst-27745 63 64 the the DET ajst-27745 63 65 sum sum NOUN ajst-27745 63 66 of of ADP ajst-27745 63 67 the the DET ajst-27745 63 68 area area NOUN ajst-27745 63 69 of of ADP ajst-27745 63 70 the the DET ajst-27745 63 71 triangle triangle NOUN ajst-27745 63 72 is be AUX ajst-27745 63 73 greater great ADJ ajst-27745 63 74 than than ADP ajst-27745 63 75 the the DET ajst-27745 63 76 boarding boarding NOUN ajst-27745 63 77 rectangle rectangle NOUN ajst-27745 63 78 area area NOUN ajst-27745 63 79 , , PUNCT ajst-27745 63 80 it it PRON ajst-27745 63 81 is be AUX ajst-27745 63 82 located locate VERB ajst-27745 63 83 outside outside ADP ajst-27745 63 84 the the DET ajst-27745 63 85 rectangle rectangle NOUN ajst-27745 63 86 , , PUNCT ajst-27745 63 87 that that ADV ajst-27745 63 88 is is ADV ajst-27745 63 89 , , PUNCT ajst-27745 63 90 the the DET ajst-27745 63 91 collision collision NOUN ajst-27745 63 92 has have AUX ajst-27745 63 93 not not PART ajst-27745 63 94 occurred occur VERB ajst-27745 63 95 . . PUNCT ajst-27745 64 1 the the DET ajst-27745 64 2 area area NOUN ajst-27745 64 3 of of ADP ajst-27745 64 4 a a DET ajst-27745 64 5 triangle triangle NOUN ajst-27745 64 6 is be AUX ajst-27745 64 7 given give VERB ajst-27745 64 8 by by ADP ajst-27745 64 9 the the DET ajst-27745 64 10 coordinates coordinate NOUN ajst-27745 64 11 of of ADP ajst-27745 64 12 three three NUM ajst-27745 64 13 points point NOUN ajst-27745 64 14 , , PUNCT ajst-27745 64 15 which which PRON ajst-27745 64 16 are be AUX ajst-27745 64 17 ( ( PUNCT ajst-27745 64 18 in in ADP ajst-27745 64 19 any any DET ajst-27745 64 20 order order NOUN ajst-27745 64 21 ) ) PUNCT ajst-27745 64 22 π‘₯ π‘₯ NOUN ajst-27745 64 23 , , PUNCT ajst-27745 64 24 𝑦 𝑦 NOUN ajst-27745 64 25 , , PUNCT ajst-27745 64 26 π‘₯ π‘₯ X ajst-27745 64 27 , , PUNCT ajst-27745 64 28 𝑦 𝑦 NOUN ajst-27745 64 29 , , PUNCT ajst-27745 64 30 π‘₯ π‘₯ X ajst-27745 64 31 , , PUNCT ajst-27745 64 32 𝑦 𝑦 NOUN ajst-27745 64 33 : : PUNCT ajst-27745 64 34 𝑆 𝑆 PROPN ajst-27745 64 35 | | ADV ajst-27745 64 36 π‘₯ π‘₯ ADP ajst-27745 64 37 π‘₯ π‘₯ X ajst-27745 64 38 𝑦 𝑦 NUM ajst-27745 64 39 𝑦 𝑦 NOUN ajst-27745 64 40 π‘₯ π‘₯ X ajst-27745 64 41 π‘₯ π‘₯ PUNCT ajst-27745 64 42 𝑦 𝑦 NUM ajst-27745 64 43 𝑦 𝑦 NOUN ajst-27745 64 44 | | NOUN ajst-27745 64 45 ( ( PUNCT ajst-27745 64 46 18 18 NUM ajst-27745 64 47 ) ) PUNCT ajst-27745 64 48 using use VERB ajst-27745 64 49 this this DET ajst-27745 64 50 model model NOUN ajst-27745 64 51 , , PUNCT ajst-27745 64 52 this this DET ajst-27745 64 53 collision collision NOUN ajst-27745 64 54 problem problem NOUN ajst-27745 64 55 is be AUX ajst-27745 64 56 converted convert VERB ajst-27745 64 57 into into ADP ajst-27745 64 58 a a DET ajst-27745 64 59 coordinate coordinate ADJ ajst-27745 64 60 solving solving NOUN ajst-27745 64 61 problem problem NOUN ajst-27745 64 62 . . PUNCT ajst-27745 65 1 from from ADP ajst-27745 65 2 the the DET ajst-27745 65 3 above above ADJ ajst-27745 65 4 analysis analysis NOUN ajst-27745 65 5 , , PUNCT ajst-27745 65 6 we we PRON ajst-27745 65 7 can can AUX ajst-27745 65 8 see see VERB ajst-27745 65 9 that that SCONJ ajst-27745 65 10 we we PRON ajst-27745 65 11 only only ADV ajst-27745 65 12 need need VERB ajst-27745 65 13 to to PART ajst-27745 65 14 determine determine VERB ajst-27745 65 15 the the DET ajst-27745 65 16 collision collision NOUN ajst-27745 65 17 of of ADP ajst-27745 65 18 the the DET ajst-27745 65 19 innermost innermost ADJ ajst-27745 65 20 circle circle NOUN ajst-27745 65 21 and and CCONJ ajst-27745 65 22 the the DET ajst-27745 65 23 penultimate penultimate NOUN ajst-27745 65 24 circle circle NOUN ajst-27745 65 25 of of ADP ajst-27745 65 26 the the DET ajst-27745 65 27 boarden boarden NOUN ajst-27745 65 28 . . PUNCT ajst-27745 66 1 the the DET ajst-27745 66 2 termination termination NOUN ajst-27745 66 3 moment moment NOUN ajst-27745 66 4 before before SCONJ ajst-27745 66 5 the the DET ajst-27745 66 6 collision collision NOUN ajst-27745 66 7 that that PRON ajst-27745 66 8 we we PRON ajst-27745 66 9 solved solve VERB ajst-27745 66 10 for for ADP ajst-27745 66 11 is be AUX ajst-27745 66 12 416.4578 416.4578 NUM ajst-27745 66 13 s. s. PROPN ajst-27745 66 14 table table NOUN ajst-27745 66 15 3 3 NUM ajst-27745 66 16 gives give VERB ajst-27745 66 17 the the DET ajst-27745 66 18 specific specific ADJ ajst-27745 66 19 positions position NOUN ajst-27745 66 20 and and CCONJ ajst-27745 66 21 velocities velocity NOUN ajst-27745 66 22 of of ADP ajst-27745 66 23 the the DET ajst-27745 66 24 benches bench NOUN ajst-27745 66 25 at at ADP ajst-27745 66 26 this this DET ajst-27745 66 27 time time NOUN ajst-27745 66 28 . . PUNCT ajst-27745 67 1 table table NOUN ajst-27745 67 2 3 3 NUM ajst-27745 67 3 . . X ajst-27745 68 1 position position NOUN ajst-27745 68 2 and and CCONJ ajst-27745 68 3 velocity velocity NOUN ajst-27745 68 4 of of ADP ajst-27745 68 5 the the DET ajst-27745 68 6 bench bench NOUN ajst-27745 68 7 at at ADP ajst-27745 68 8 the the DET ajst-27745 68 9 moment moment NOUN ajst-27745 68 10 of of ADP ajst-27745 68 11 termination termination NOUN ajst-27745 68 12 of of ADP ajst-27745 68 13 the the DET ajst-27745 68 14 collision collision NOUN ajst-27745 68 15 horizontal horizontal ADJ ajst-27745 68 16 coordinate coordinate NOUN ajst-27745 68 17 x x SYM ajst-27745 68 18 ( ( PUNCT ajst-27745 68 19 m m NOUN ajst-27745 68 20 ) ) PUNCT ajst-27745 68 21 vertical vertical ADJ ajst-27745 68 22 coordinate coordinate NOUN ajst-27745 68 23 y y PROPN ajst-27745 68 24 ( ( PUNCT ajst-27745 68 25 m m NOUN ajst-27745 68 26 ) ) PUNCT ajst-27745 68 27 velocity velocity NOUN ajst-27745 68 28 ( ( PUNCT ajst-27745 68 29 m m NOUN ajst-27745 68 30 / / SYM ajst-27745 68 31 s s NOUN ajst-27745 68 32 ) ) PUNCT ajst-27745 68 33 mixer mixer NOUN ajst-27745 68 34 1.889317 1.889317 NUM ajst-27745 68 35 -1.03866 -1.03866 NOUN ajst-27745 68 36 1.000000 1.000000 NUM ajst-27745 68 37 section section NOUN ajst-27745 68 38 1 1 NUM ajst-27745 68 39 of of ADP ajst-27745 68 40 the the DET ajst-27745 68 41 dragon dragon NOUN ajst-27745 68 42 's 's PART ajst-27745 68 43 body body NOUN ajst-27745 68 44 1.4206261.781327 1.4206261.781327 NOUN ajst-27745 68 45 0.988705 0.988705 NUM ajst-27745 68 46 section section NOUN ajst-27745 68 47 51 51 NUM ajst-27745 68 48 of of ADP ajst-27745 68 49 the the DET ajst-27745 68 50 dragon dragon NOUN ajst-27745 68 51 's 's PART ajst-27745 68 52 body body NOUN ajst-27745 68 53 4.494389 4.494389 NUM ajst-27745 68 54 3.263509 3.263509 NUM ajst-27745 68 55 0.924827 0.924827 NUM ajst-27745 68 56 section section NOUN ajst-27745 68 57 101 101 NUM ajst-27745 68 58 of of ADP ajst-27745 68 59 the the DET ajst-27745 68 60 dragon dragon NOUN ajst-27745 68 61 's 's PART ajst-27745 68 62 body body NOUN ajst-27745 68 63 -5.552990 -5.552990 NOUN ajst-27745 68 64 -5.02482 -5.02482 PROPN ajst-27745 68 65 0.920103 0.920103 NUM ajst-27745 68 66 section section NOUN ajst-27745 68 67 151 151 NUM ajst-27745 68 68 of of ADP ajst-27745 68 69 the the DET ajst-27745 68 70 dragon dragon NOUN ajst-27745 68 71 's 's PART ajst-27745 68 72 body body NOUN ajst-27745 68 73 8.233446 8.233446 NUM ajst-27745 68 74 0.616415 0.616415 NUM ajst-27745 68 75 0.918579 0.918579 NUM ajst-27745 68 76 section section NOUN ajst-27745 68 77 201 201 NUM ajst-27745 68 78 of of ADP ajst-27745 68 79 the the DET ajst-27745 68 80 dragon dragon NOUN ajst-27745 68 81 's 's PART ajst-27745 68 82 body body NOUN ajst-27745 68 83 8.056790 8.056790 NUM ajst-27745 68 84 2.695702 2.695702 NUM ajst-27745 68 85 0.916375 0.916375 NUM ajst-27745 68 86 dragon dragon NOUN ajst-27745 68 87 's 's PART ajst-27745 68 88 tail tail NOUN ajst-27745 68 89 8.7005811233970 8.7005811233970 NUM ajst-27745 68 90 1233970 1233970 NUM ajst-27745 68 91 0.914978 0.914978 NUM ajst-27745 68 92 301 301 NUM ajst-27745 68 93 4 4 NUM ajst-27745 68 94 . . PUNCT ajst-27745 68 95 conclusions conclusion NOUN ajst-27745 68 96 in in ADP ajst-27745 68 97 this this DET ajst-27745 68 98 paper paper NOUN ajst-27745 68 99 , , PUNCT ajst-27745 68 100 we we PRON ajst-27745 68 101 propose propose VERB ajst-27745 68 102 a a DET ajst-27745 68 103 mathematical mathematical ADJ ajst-27745 68 104 model model NOUN ajst-27745 68 105 based base VERB ajst-27745 68 106 on on ADP ajst-27745 68 107 isometric isometric ADJ ajst-27745 68 108 solenoids solenoid NOUN ajst-27745 68 109 and and CCONJ ajst-27745 68 110 discrete discrete ADJ ajst-27745 68 111 simulation simulation NOUN ajst-27745 68 112 by by ADP ajst-27745 68 113 studying study VERB ajst-27745 68 114 the the DET ajst-27745 68 115 position position NOUN ajst-27745 68 116 , , PUNCT ajst-27745 68 117 velocity velocity NOUN ajst-27745 68 118 change change NOUN ajst-27745 68 119 and and CCONJ ajst-27745 68 120 collision collision NOUN ajst-27745 68 121 detection detection NOUN ajst-27745 68 122 problems problem NOUN ajst-27745 68 123 during during ADP ajst-27745 68 124 the the DET ajst-27745 68 125 traveling travel VERB ajst-27745 68 126 process process NOUN ajst-27745 68 127 of of ADP ajst-27745 68 128 the the DET ajst-27745 68 129 bench bench NOUN ajst-27745 68 130 dragon dragon NOUN ajst-27745 68 131 . . PUNCT ajst-27745 69 1 first first ADV ajst-27745 69 2 , , PUNCT ajst-27745 69 3 we we PRON ajst-27745 69 4 calculate calculate VERB ajst-27745 69 5 the the DET ajst-27745 69 6 position position NOUN ajst-27745 69 7 of of ADP ajst-27745 69 8 each each DET ajst-27745 69 9 section section NOUN ajst-27745 69 10 of of ADP ajst-27745 69 11 the the DET ajst-27745 69 12 bench bench NOUN ajst-27745 69 13 during during ADP ajst-27745 69 14 the the DET ajst-27745 69 15 traveling travel VERB ajst-27745 69 16 process process NOUN ajst-27745 69 17 of of ADP ajst-27745 69 18 the the DET ajst-27745 69 19 bench bench NOUN ajst-27745 69 20 dragon dragon NOUN ajst-27745 69 21 by by ADP ajst-27745 69 22 iterative iterative NOUN ajst-27745 69 23 recursion recursion NOUN ajst-27745 69 24 using use VERB ajst-27745 69 25 the the DET ajst-27745 69 26 equations equation NOUN ajst-27745 69 27 of of ADP ajst-27745 69 28 isometric isometric ADJ ajst-27745 69 29 solenoids solenoid NOUN ajst-27745 69 30 and and CCONJ ajst-27745 69 31 the the DET ajst-27745 69 32 robotic robotic ADJ ajst-27745 69 33 arm arm NOUN ajst-27745 69 34 model model NOUN ajst-27745 69 35 . . PUNCT ajst-27745 70 1 this this DET ajst-27745 70 2 method method NOUN ajst-27745 70 3 not not PART ajst-27745 70 4 only only ADV ajst-27745 70 5 takes take VERB ajst-27745 70 6 into into ADP ajst-27745 70 7 account account NOUN ajst-27745 70 8 the the DET ajst-27745 70 9 physical physical ADJ ajst-27745 70 10 structure structure NOUN ajst-27745 70 11 of of ADP ajst-27745 70 12 the the DET ajst-27745 70 13 bench bench NOUN ajst-27745 70 14 dragon dragon NOUN ajst-27745 70 15 , , PUNCT ajst-27745 70 16 but but CCONJ ajst-27745 70 17 also also ADV ajst-27745 70 18 makes make VERB ajst-27745 70 19 full full ADJ ajst-27745 70 20 use use NOUN ajst-27745 70 21 of of ADP ajst-27745 70 22 the the DET ajst-27745 70 23 mathematical mathematical ADJ ajst-27745 70 24 properties property NOUN ajst-27745 70 25 of of ADP ajst-27745 70 26 isometric isometric ADJ ajst-27745 70 27 solenoids solenoid NOUN ajst-27745 70 28 , , PUNCT ajst-27745 70 29 so so SCONJ ajst-27745 70 30 that that SCONJ ajst-27745 70 31 the the DET ajst-27745 70 32 bench bench NOUN ajst-27745 70 33 dragon dragon NOUN ajst-27745 70 34 can can AUX ajst-27745 70 35 maintain maintain VERB ajst-27745 70 36 uniform uniform ADJ ajst-27745 70 37 speed speed NOUN ajst-27745 70 38 and and CCONJ ajst-27745 70 39 smooth smooth ADJ ajst-27745 70 40 dynamics dynamic NOUN ajst-27745 70 41 during during ADP ajst-27745 70 42 the the DET ajst-27745 70 43 traveling travel VERB ajst-27745 70 44 process process NOUN ajst-27745 70 45 . . PUNCT ajst-27745 71 1 then then ADV ajst-27745 71 2 , , PUNCT ajst-27745 71 3 we we PRON ajst-27745 71 4 further far ADV ajst-27745 71 5 optimize optimize VERB ajst-27745 71 6 the the DET ajst-27745 71 7 position position NOUN ajst-27745 71 8 solution solution NOUN ajst-27745 71 9 process process NOUN ajst-27745 71 10 of of ADP ajst-27745 71 11 the the DET ajst-27745 71 12 bench bench NOUN ajst-27745 71 13 dragon dragon NOUN ajst-27745 71 14 by by ADP ajst-27745 71 15 combining combine VERB ajst-27745 71 16 the the DET ajst-27745 71 17 velocity velocity NOUN ajst-27745 71 18 analysis analysis NOUN ajst-27745 71 19 of of ADP ajst-27745 71 20 rigid rigid ADJ ajst-27745 71 21 body body NOUN ajst-27745 71 22 rod rod NOUN ajst-27745 71 23 . . PUNCT ajst-27745 72 1 by by ADP ajst-27745 72 2 introducing introduce VERB ajst-27745 72 3 the the DET ajst-27745 72 4 rigid rigid ADJ ajst-27745 72 5 - - PUNCT ajst-27745 72 6 body body NOUN ajst-27745 72 7 rod rod NOUN ajst-27745 72 8 model model NOUN ajst-27745 72 9 , , PUNCT ajst-27745 72 10 we we PRON ajst-27745 72 11 are be AUX ajst-27745 72 12 able able ADJ ajst-27745 72 13 to to PART ajst-27745 72 14 more more ADV ajst-27745 72 15 accurately accurately ADV ajst-27745 72 16 analyze analyze VERB ajst-27745 72 17 the the DET ajst-27745 72 18 velocity velocity NOUN ajst-27745 72 19 and and CCONJ ajst-27745 72 20 acceleration acceleration NOUN ajst-27745 72 21 changes change NOUN ajst-27745 72 22 of of ADP ajst-27745 72 23 the the DET ajst-27745 72 24 bench bench NOUN ajst-27745 72 25 dragon dragon NOUN ajst-27745 72 26 during during ADP ajst-27745 72 27 the the DET ajst-27745 72 28 traveling travel VERB ajst-27745 72 29 process process NOUN ajst-27745 72 30 , , PUNCT ajst-27745 72 31 which which PRON ajst-27745 72 32 provides provide VERB ajst-27745 72 33 more more ADV ajst-27745 72 34 specific specific ADJ ajst-27745 72 35 operational operational ADJ ajst-27745 72 36 guidance guidance NOUN ajst-27745 72 37 for for ADP ajst-27745 72 38 the the DET ajst-27745 72 39 dragon dragon NOUN ajst-27745 72 40 dancers dancer NOUN ajst-27745 72 41 . . PUNCT ajst-27745 73 1 in in ADP ajst-27745 73 2 addition addition NOUN ajst-27745 73 3 , , PUNCT ajst-27745 73 4 we we PRON ajst-27745 73 5 also also ADV ajst-27745 73 6 consider consider VERB ajst-27745 73 7 the the DET ajst-27745 73 8 collision collision NOUN ajst-27745 73 9 problem problem NOUN ajst-27745 73 10 that that SCONJ ajst-27745 73 11 the the DET ajst-27745 73 12 bench bench NOUN ajst-27745 73 13 dragon dragon NOUN ajst-27745 73 14 may may AUX ajst-27745 73 15 encounter encounter VERB ajst-27745 73 16 during during ADP ajst-27745 73 17 the the DET ajst-27745 73 18 marching marching NOUN ajst-27745 73 19 process process NOUN ajst-27745 73 20 , , PUNCT ajst-27745 73 21 and and CCONJ ajst-27745 73 22 through through ADP ajst-27745 73 23 discrete discrete ADJ ajst-27745 73 24 simulation simulation NOUN ajst-27745 73 25 technology technology NOUN ajst-27745 73 26 , , PUNCT ajst-27745 73 27 we we PRON ajst-27745 73 28 discretize discretize VERB ajst-27745 73 29 the the DET ajst-27745 73 30 trajectory trajectory NOUN ajst-27745 73 31 of of ADP ajst-27745 73 32 the the DET ajst-27745 73 33 disk disk NOUN ajst-27745 73 34 entry entry NOUN ajst-27745 73 35 and and CCONJ ajst-27745 73 36 perform perform VERB ajst-27745 73 37 collision collision NOUN ajst-27745 73 38 detection detection NOUN ajst-27745 73 39 , , PUNCT ajst-27745 73 40 so so SCONJ ajst-27745 73 41 as as SCONJ ajst-27745 73 42 to to PART ajst-27745 73 43 obtain obtain VERB ajst-27745 73 44 key key ADJ ajst-27745 73 45 information information NOUN ajst-27745 73 46 such such ADJ ajst-27745 73 47 as as ADP ajst-27745 73 48 the the DET ajst-27745 73 49 time time NOUN ajst-27745 73 50 , , PUNCT ajst-27745 73 51 position position NOUN ajst-27745 73 52 and and CCONJ ajst-27745 73 53 speed speed NOUN ajst-27745 73 54 of of ADP ajst-27745 73 55 the the DET ajst-27745 73 56 termination termination NOUN ajst-27745 73 57 moment moment NOUN ajst-27745 73 58 . . PUNCT ajst-27745 74 1 this this PRON ajst-27745 74 2 not not PART ajst-27745 74 3 only only ADV ajst-27745 74 4 improves improve VERB ajst-27745 74 5 the the DET ajst-27745 74 6 safety safety NOUN ajst-27745 74 7 of of ADP ajst-27745 74 8 the the DET ajst-27745 74 9 bench bench NOUN ajst-27745 74 10 dragon dragon NOUN ajst-27745 74 11 performance performance NOUN ajst-27745 74 12 , , PUNCT ajst-27745 74 13 but but CCONJ ajst-27745 74 14 also also ADV ajst-27745 74 15 provides provide VERB ajst-27745 74 16 an an DET ajst-27745 74 17 important important ADJ ajst-27745 74 18 reference reference NOUN ajst-27745 74 19 for for ADP ajst-27745 74 20 the the DET ajst-27745 74 21 optimization optimization NOUN ajst-27745 74 22 of of ADP ajst-27745 74 23 the the DET ajst-27745 74 24 performance performance NOUN ajst-27745 74 25 . . PUNCT ajst-27745 75 1 in in ADP ajst-27745 75 2 summary summary NOUN ajst-27745 75 3 , , PUNCT ajst-27745 75 4 the the DET ajst-27745 75 5 model model NOUN ajst-27745 75 6 proposed propose VERB ajst-27745 75 7 in in ADP ajst-27745 75 8 this this DET ajst-27745 75 9 paper paper NOUN ajst-27745 75 10 can can AUX ajst-27745 75 11 effectively effectively ADV ajst-27745 75 12 solve solve VERB ajst-27745 75 13 the the DET ajst-27745 75 14 optimization optimization NOUN ajst-27745 75 15 problem problem NOUN ajst-27745 75 16 in in ADP ajst-27745 75 17 the the DET ajst-27745 75 18 process process NOUN ajst-27745 75 19 of of ADP ajst-27745 75 20 bench bench NOUN ajst-27745 75 21 dragon dragon NOUN ajst-27745 75 22 marching marching NOUN ajst-27745 75 23 and and CCONJ ajst-27745 75 24 provide provide VERB ajst-27745 75 25 scientific scientific ADJ ajst-27745 75 26 theoretical theoretical ADJ ajst-27745 75 27 support support NOUN ajst-27745 75 28 for for ADP ajst-27745 75 29 the the DET ajst-27745 75 30 smooth smooth ADJ ajst-27745 75 31 progress progress NOUN ajst-27745 75 32 of of ADP ajst-27745 75 33 bench bench NOUN ajst-27745 75 34 dragon dragon NOUN ajst-27745 75 35 performance performance NOUN ajst-27745 75 36 . . PUNCT ajst-27745 76 1 through through ADP ajst-27745 76 2 the the DET ajst-27745 76 3 application application NOUN ajst-27745 76 4 of of ADP ajst-27745 76 5 mathematical mathematical ADJ ajst-27745 76 6 modeling modeling NOUN ajst-27745 76 7 and and CCONJ ajst-27745 76 8 simulation simulation NOUN ajst-27745 76 9 technology technology NOUN ajst-27745 76 10 , , PUNCT ajst-27745 76 11 we we PRON ajst-27745 76 12 can can AUX ajst-27745 76 13 not not PART ajst-27745 76 14 only only ADV ajst-27745 76 15 improve improve VERB ajst-27745 76 16 the the DET ajst-27745 76 17 artistic artistic ADJ ajst-27745 76 18 effect effect NOUN ajst-27745 76 19 of of ADP ajst-27745 76 20 the the DET ajst-27745 76 21 bench bench NOUN ajst-27745 76 22 dragon dragon NOUN ajst-27745 76 23 performance performance NOUN ajst-27745 76 24 , , PUNCT ajst-27745 76 25 but but CCONJ ajst-27745 76 26 also also ADV ajst-27745 76 27 ensure ensure VERB ajst-27745 76 28 the the DET ajst-27745 76 29 safety safety NOUN ajst-27745 76 30 and and CCONJ ajst-27745 76 31 ornamental ornamental ADJ ajst-27745 76 32 performance performance NOUN ajst-27745 76 33 . . PUNCT ajst-27745 77 1 in in ADP ajst-27745 77 2 the the DET ajst-27745 77 3 future future NOUN ajst-27745 77 4 , , PUNCT ajst-27745 77 5 we we PRON ajst-27745 77 6 will will AUX ajst-27745 77 7 continue continue VERB ajst-27745 77 8 to to PART ajst-27745 77 9 study study VERB ajst-27745 77 10 the the DET ajst-27745 77 11 dynamics dynamic NOUN ajst-27745 77 12 of of ADP ajst-27745 77 13 the the DET ajst-27745 77 14 bench bench NOUN ajst-27745 77 15 dragon dragon NOUN ajst-27745 77 16 and and CCONJ ajst-27745 77 17 explore explore VERB ajst-27745 77 18 more more ADJ ajst-27745 77 19 ways way NOUN ajst-27745 77 20 to to PART ajst-27745 77 21 optimize optimize VERB ajst-27745 77 22 the the DET ajst-27745 77 23 bench bench NOUN ajst-27745 77 24 dragon dragon NOUN ajst-27745 77 25 performance performance NOUN ajst-27745 77 26 , , PUNCT ajst-27745 77 27 so so SCONJ ajst-27745 77 28 as as SCONJ ajst-27745 77 29 to to PART ajst-27745 77 30 make make VERB ajst-27745 77 31 greater great ADJ ajst-27745 77 32 contributions contribution NOUN ajst-27745 77 33 to to ADP ajst-27745 77 34 the the DET ajst-27745 77 35 inheritance inheritance NOUN ajst-27745 77 36 and and CCONJ ajst-27745 77 37 development development NOUN ajst-27745 77 38 of of ADP ajst-27745 77 39 chinese chinese ADJ ajst-27745 77 40 traditional traditional ADJ ajst-27745 77 41 folk folk NOUN ajst-27745 77 42 culture culture NOUN ajst-27745 77 43 . . PUNCT ajst-27745 78 1 references reference NOUN ajst-27745 78 2 [ [ X ajst-27745 78 3 1 1 NUM ajst-27745 78 4 ] ] X ajst-27745 78 5 chen chen PROPN ajst-27745 78 6 , , PUNCT ajst-27745 78 7 k. k. PROPN ajst-27745 79 1 c c X ajst-27745 79 2 .. .. PUNCT ajst-27745 79 3 the the DET ajst-27745 79 4 living live VERB ajst-27745 79 5 bench bench NOUN ajst-27745 79 6 dragon dragon NOUN ajst-27745 79 7 : : PUNCT ajst-27745 79 8 shaping shape VERB ajst-27745 79 9 china china PROPN ajst-27745 79 10 's 's PART ajst-27745 79 11 indigenous indigenous ADJ ajst-27745 79 12 tree tree NOUN ajst-27745 79 13 burial burial NOUN ajst-27745 79 14 model model NOUN ajst-27745 79 15 with with ADP ajst-27745 79 16 ritual ritual ADJ ajst-27745 79 17 design[j design[j PROPN ajst-27745 79 18 ] ] PUNCT ajst-27745 79 19 . . PUNCT ajst-27745 80 1 landscape landscape NOUN ajst-27745 80 2 architecture architecture NOUN ajst-27745 80 3 ( ( PUNCT ajst-27745 80 4 in in ADP ajst-27745 80 5 chinese chinese ADJ ajst-27745 80 6 and and CCONJ ajst-27745 80 7 english english PROPN ajst-27745 80 8 ) ) PUNCT ajst-27745 80 9 , , PUNCT ajst-27745 80 10 2022 2022 NUM ajst-27745 80 11 , , PUNCT ajst-27745 80 12 10(04 10(04 NUM ajst-27745 80 13 ): ): PUNCT ajst-27745 80 14 96-108.fangfang 96-108.fangfang PROPN ajst-27745 80 15 . . PUNCT ajst-27745 81 1 research research NOUN ajst-27745 81 2 on on ADP ajst-27745 81 3 power power NOUN ajst-27745 81 4 load load NOUN ajst-27745 81 5 forecasting forecasting NOUN ajst-27745 81 6 based base VERB ajst-27745 81 7 on on ADP ajst-27745 81 8 improved improved ADJ ajst-27745 81 9 bp bp PROPN ajst-27745 81 10 neural neural ADJ ajst-27745 81 11 network network NOUN ajst-27745 82 1 [ [ X ajst-27745 82 2 d d X ajst-27745 82 3 ] ] X ajst-27745 82 4 . . PUNCT ajst-27745 83 1 harbin harbin PROPN ajst-27745 83 2 institute institute PROPN ajst-27745 83 3 of of ADP ajst-27745 83 4 technology technology PROPN ajst-27745 83 5 , , PUNCT ajst-27745 83 6 2011 2011 NUM ajst-27745 83 7 . . PUNCT ajst-27745 84 1 [ [ X ajst-27745 84 2 2 2 NUM ajst-27745 84 3 ] ] X ajst-27745 84 4 liu liu PROPN ajst-27745 84 5 chuanwen chuanwen PROPN ajst-27745 84 6 , , PUNCT ajst-27745 84 7 cheng cheng PROPN ajst-27745 84 8 fuchao fuchao PROPN ajst-27745 84 9 . . PUNCT ajst-27745 85 1 research research NOUN ajst-27745 85 2 on on ADP ajst-27745 85 3 cultural cultural ADJ ajst-27745 85 4 memory memory NOUN ajst-27745 85 5 of of ADP ajst-27745 85 6 pujiang pujiang PROPN ajst-27745 85 7 bench bench NOUN ajst-27745 85 8 dragon dragon NOUN ajst-27745 85 9 under under ADP ajst-27745 85 10 the the DET ajst-27745 85 11 perspective perspective NOUN ajst-27745 85 12 of of ADP ajst-27745 85 13 cultural cultural ADJ ajst-27745 85 14 confidence[j confidence[j NOUN ajst-27745 85 15 ] ] PUNCT ajst-27745 85 16 . . PUNCT ajst-27745 86 1 new new PROPN ajst-27745 86 2 legend,2024,(22):100 legend,2024,(22):100 PROPN ajst-27745 86 3 - - PUNCT ajst-27745 86 4 102 102 NUM ajst-27745 86 5 . . PUNCT ajst-27745 87 1 [ [ X ajst-27745 87 2 3 3 X ajst-27745 87 3 ] ] SYM ajst-27745 87 4 hu hu PROPN ajst-27745 87 5 yang yang PROPN ajst-27745 87 6 . . PUNCT ajst-27745 88 1 study study NOUN ajst-27745 88 2 on on ADP ajst-27745 88 3 the the DET ajst-27745 88 4 development development NOUN ajst-27745 88 5 of of ADP ajst-27745 88 6 cultural cultural ADJ ajst-27745 88 7 festival festival PROPN ajst-27745 88 8 tourism tourism NOUN ajst-27745 88 9 of of ADP ajst-27745 88 10 hakka hakka PROPN ajst-27745 88 11 dragon dragon PROPN ajst-27745 88 12 dance dance NOUN ajst-27745 88 13 in in ADP ajst-27745 88 14 northeastern northeastern ADJ ajst-27745 88 15 sichuan sichuan PROPN ajst-27745 88 16 - - PUNCT ajst-27745 88 17 taking take VERB ajst-27745 88 18 the the DET ajst-27745 88 19 national national ADJ ajst-27745 88 20 β€œ " PUNCT ajst-27745 88 21 nonproducts nonproduct NOUN ajst-27745 88 22 ” " PUNCT ajst-27745 88 23 anren anren PROPN ajst-27745 88 24 township township NOUN ajst-27745 88 25 bench bench NOUN ajst-27745 88 26 dragon dragon NOUN ajst-27745 88 27 as as ADP ajst-27745 88 28 an an DET ajst-27745 88 29 example[j example[j NOUN ajst-27745 88 30 ] ] PUNCT ajst-27745 88 31 . . PUNCT ajst-27745 89 1 wushu wushu NOUN ajst-27745 89 2 research,2024,9(01):121124 research,2024,9(01):121124 PROPN ajst-27745 89 3 . . PUNCT ajst-27745 90 1 [ [ X ajst-27745 90 2 4 4 NUM ajst-27745 90 3 ] ] ADJ ajst-27745 90 4 principle principle NOUN ajst-27745 90 5 and and CCONJ ajst-27745 90 6 calculation calculation NOUN ajst-27745 90 7 of of ADP ajst-27745 90 8 isometric isometric ADJ ajst-27745 90 9 spiral[j spiral[j PROPN ajst-27745 90 10 ] ] PUNCT ajst-27745 90 11 . . PUNCT ajst-27745 91 1 practice practice NOUN ajst-27745 91 2 and and CCONJ ajst-27745 91 3 understanding understanding NOUN ajst-27745 91 4 of of ADP ajst-27745 91 5 mathematics,2018,48(11):165 mathematics,2018,48(11):165 NOUN ajst-27745 91 6 - - PUNCT ajst-27745 91 7 174 174 NUM ajst-27745 91 8 . . PUNCT ajst-27745 92 1 [ [ X ajst-27745 92 2 5 5 NUM ajst-27745 92 3 ] ] PUNCT ajst-27745 92 4 tu tu PROPN ajst-27745 92 5 dx dx PROPN ajst-27745 92 6 , , PUNCT ajst-27745 92 7 jiang jiang PROPN ajst-27745 92 8 fj fj PROPN ajst-27745 92 9 . . PUNCT ajst-27745 93 1 a a DET ajst-27745 93 2 preliminary preliminary ADJ ajst-27745 93 3 investigation investigation NOUN ajst-27745 93 4 of of ADP ajst-27745 93 5 the the DET ajst-27745 93 6 mathematical mathematical ADJ ajst-27745 93 7 properties property NOUN ajst-27745 93 8 of of ADP ajst-27745 93 9 isometric isometric ADJ ajst-27745 93 10 conic conic ADJ ajst-27745 93 11 spirals[j spirals[j NOUN ajst-27745 93 12 ] ] PUNCT ajst-27745 93 13 . . PUNCT ajst-27745 94 1 physics physics PROPN ajst-27745 94 2 bulletin,2018,(12):75 bulletin,2018,(12):75 PROPN ajst-27745 94 3 - - PUNCT ajst-27745 94 4 77 77 NUM ajst-27745 94 5 . . PUNCT ajst-27745 95 1 [ [ X ajst-27745 95 2 6 6 NUM ajst-27745 95 3 ] ] X ajst-27745 95 4 chen chen PROPN ajst-27745 95 5 yuanning yuanning PROPN ajst-27745 95 6 . . PUNCT ajst-27745 96 1 some some DET ajst-27745 96 2 studies study NOUN ajst-27745 96 3 on on ADP ajst-27745 96 4 isometric isometric ADJ ajst-27745 96 5 curves[d curves[d PROPN ajst-27745 96 6 ] ] PUNCT ajst-27745 96 7 . . PUNCT ajst-27745 97 1 hefei hefei PROPN ajst-27745 97 2 university university PROPN ajst-27745 97 3 of of ADP ajst-27745 97 4 technology,2007 technology,2007 PROPN ajst-27745 97 5 . . PUNCT ajst-27745 98 1 [ [ X ajst-27745 98 2 7 7 X ajst-27745 98 3 ] ] X ajst-27745 98 4 lu lu PROPN ajst-27745 98 5 jianpeng jianpeng PROPN ajst-27745 98 6 . . PUNCT ajst-27745 99 1 research research NOUN ajst-27745 99 2 on on ADP ajst-27745 99 3 multi multi ADJ ajst-27745 99 4 - - NOUN ajst-27745 99 5 degree degree NOUN ajst-27745 99 6 - - PUNCT ajst-27745 99 7 of of ADP ajst-27745 99 8 - - PUNCT ajst-27745 99 9 freedom freedom NOUN ajst-27745 99 10 pseudorigid pseudorigid ADJ ajst-27745 99 11 body body NOUN ajst-27745 99 12 model model NOUN ajst-27745 99 13 of of ADP ajst-27745 99 14 flexible flexible ADJ ajst-27745 99 15 mechanism mechanism NOUN ajst-27745 99 16 with with ADP ajst-27745 99 17 axial axial ADJ ajst-27745 99 18 deformation deformation NOUN ajst-27745 100 1 [ [ X ajst-27745 100 2 d d X ajst-27745 100 3 ] ] X ajst-27745 100 4 . . PUNCT ajst-27745 101 1 north north NOUN ajst-27745 101 2 central central ADJ ajst-27745 101 3 university,2016 university,2016 NOUN ajst-27745 101 4 . . PUNCT ajst-27745 102 1 [ [ X ajst-27745 102 2 8 8 NUM ajst-27745 102 3 ] ] PUNCT ajst-27745 102 4 taiyong taiyong NOUN ajst-27745 102 5 wang wang PROPN ajst-27745 102 6 , , PUNCT ajst-27745 102 7 zhongtong zhongtong VERB ajst-27745 102 8 you you PRON ajst-27745 102 9 , , PUNCT ajst-27745 102 10 quanqi quanqi VERB ajst-27745 102 11 xin xin PROPN ajst-27745 102 12 . . PUNCT ajst-27745 103 1 helix helix ADJ ajst-27745 103 2 interpolation interpolation NOUN ajst-27745 103 3 velocity velocity NOUN ajst-27745 103 4 planning planning NOUN ajst-27745 103 5 and and CCONJ ajst-27745 103 6 its its PRON ajst-27745 103 7 interpolation interpolation NOUN ajst-27745 103 8 parameter parameter NOUN ajst-27745 103 9 solution solution NOUN ajst-27745 103 10 method[j method[j PROPN ajst-27745 103 11 ] ] PUNCT ajst-27745 103 12 . . PUNCT ajst-27745 104 1 journal journal PROPN ajst-27745 104 2 of of ADP ajst-27745 104 3 tianjin tianjin PROPN ajst-27745 104 4 university university PROPN ajst-27745 104 5 ( ( PUNCT ajst-27745 104 6 natural natural ADJ ajst-27745 104 7 science science NOUN ajst-27745 104 8 and and CCONJ ajst-27745 104 9 engineering engineering NOUN ajst-27745 104 10 technology technology NOUN ajst-27745 104 11 edition edition NOUN ajst-27745 104 12 ) ) PUNCT ajst-27745 104 13 , , PUNCT ajst-27745 104 14 2018 2018 NUM ajst-27745 104 15 , , PUNCT ajst-27745 104 16 51(11 51(11 NUM ajst-27745 104 17 ): ): PUNCT ajst-27745 104 18 1107 1107 NUM ajst-27745 104 19 - - SYM ajst-27745 104 20 1116 1116 NUM ajst-27745 104 21 . . PUNCT ajst-27745 105 1 [ [ X ajst-27745 105 2 9 9 NUM ajst-27745 105 3 ] ] PUNCT ajst-27745 105 4 he he PRON ajst-27745 105 5 peng peng PROPN ajst-27745 105 6 , , PUNCT ajst-27745 105 7 xu xu PROPN ajst-27745 105 8 shuhua shuhua PROPN ajst-27745 105 9 , , PUNCT ajst-27745 105 10 jiang jiang PROPN ajst-27745 105 11 bo bo PROPN ajst-27745 105 12 . . PUNCT ajst-27745 106 1 mathematical mathematical PROPN ajst-27745 106 2 simulation simulation NOUN ajst-27745 106 3 of of ADP ajst-27745 106 4 mill mill NOUN ajst-27745 106 5 extruder extruder NOUN ajst-27745 106 6 based base VERB ajst-27745 106 7 on on ADP ajst-27745 106 8 archimedean archimedean PROPN ajst-27745 106 9 spiral[j spiral[j PROPN ajst-27745 106 10 ] ] PUNCT ajst-27745 106 11 . . PUNCT ajst-27745 107 1 plastics plastic NOUN ajst-27745 107 2 , , PUNCT ajst-27745 107 3 2003 2003 NUM ajst-27745 107 4 , , PUNCT ajst-27745 107 5 ( ( PUNCT ajst-27745 107 6 02 02 NUM ajst-27745 107 7 ): ): PUNCT ajst-27745 107 8 60 60 NUM ajst-27745 107 9 - - SYM ajst-27745 107 10 64 64 NUM ajst-27745 107 11 . . PUNCT