id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cte-761	Flehantov, Leonid O.; Ovsiienko, Yuliia I.; Antonets, Anatolii V.	Enhancing mathematical modelling education at agricultural universities: A comparative study of dynamic vector diagrams using GeoGebra	2025	18	.pdf	application/pdf	5352	270	37	The vectors of gravitational force 𝐹3_𝑇 , air resistance force 𝐹3_𝑟, and Magnus force 𝐹3_𝑀 for model MM III are represented as: F3_T=Vector(C,F3_1), F3_r=Vector(C,F3_2), F3_M=Vector(C,F3_4) Through this implementation, students created mathematical models MM [0, 𝑡𝑀 ] , 𝑖 = 0, 𝑛 – observation time points • 𝑖 – position observation index • 𝑛 – number of observation points • Δ𝑡 = 𝑡𝑀/𝑛 – time interval between observations (s) • 𝑡𝑀 – simulation duration (s) • 𝑥𝑖 = 𝑥(𝑡𝑖), 𝑦𝑖 = 𝑦(𝑡𝑖) – object centre coordinates at time 𝑡𝑖 • 𝑣𝑥𝑖 = 𝑣𝑥(𝑡𝑖), 𝑣𝑦𝑖 = 𝑣𝑦(𝑡𝑖) – velocity projections at time 𝑡𝑖 • 𝑣𝑖 = √︁ 𝑣2𝑥𝑖 + 𝑣2𝑦𝑖 – object velocity magnitude at time 𝑡𝑖 Models MM II (equations 1 and 3) and MM III (equations 1 and 4), unlike MM I, lack analytical solutions.	cache/cte-761.pdf	txt/cte-761.txt