id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
bibechana-9310	Hassan, MR; Thapa, RR	Periodic Solution of the restricted three body problem	2013	8	.pdf	application/pdf	3576	140	77	Yx x y 2 2 r r ∈ −µ µ = + + − − + − − (4) Limiting case µ=0 For the elimination of singularity at the bigger primary we shall use Levi-Civita's [6] variables as used by Kurcheeva: ( ) ( ) 2 x iy p iq P iQ X i Y 2(P iq) +µ + = + − − +µ = + (5) ( )2 2dt 4 p q ds = + (6) The regularized canonical equations of motion became dp dq , dS P dS Q dP dQ , dS p dS q ∂Ω ∂Ω = = ∂ ∂ ∂Ω ∂Ω = = ∂ ∂ (7) where ( ) ( ) ( ) ( ) ( ) 2 2 4 4 1 1 2 3 4 4 1 1 1 P Q 2r qP pQ 4 p q 4 4 4 r / r 2 2Cr 2 'r 4 ' p q Ω = + + − + µ − − + µ − µ + − ∈ − µ∈ − (8) M.R. Hassan and R.R.Thapa / BIBECHANA 10 (2014) 44-51: BMHSS, p.46 (Online Publication: Dec., 2013) ( ) ( )22 2 2 2 2 2 2 1 2r p q , r 1 2 p q p q= + = − + + + (9) 2,k even, m odd.φ = ω = ±π − − For arbitrary k and m, there exist periodic solutions reducing to the generating one for 0.µ = The period of these solutions is an analytic function of µ , S=S*+4S(µ ), S* being the period of the generating solution.	cache/bibechana-9310.pdf	txt/bibechana-9310.txt