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On the perturbed restricted three-body problem

\ddot{X}=\dfrac{\partial V}{\partial X}. \end{array}$$ (9) m Y ¨ = ∂ V ∂ Y . $$\begin{array}{} \displaystyle m\ddot{Y}=\dfrac{\partial V}{\partial Y}. \end{array}$$ (10) From Eq. ( 3 ), the potential V 1 between m and m 1 is given by V 1 = − G m m 1 [ 1 r 1 + A 1 + A 2 r 1 3 ] , $$\begin{array}{} \displaystyle V_{1}=-Gmm_1\Bigg[\dfrac{1}{r_1}+\dfrac{A_1+A}{2r_1^3}\Bigg], \end{array}$$ (11) and the potential V between m, m 1 and m 2 is also given by V 2 = − G m m 2 [ 1 r 2 + A 2 + A 2 r 2 3 ] , $$\begin{array}{} \displaystyle V_{2}=-Gmm_2\Bigg[\dfrac{1}{r

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