Question: For the two body central-force problem with a Newtonian potential, the effective two-dimensional orbit dynamics can be described by the Lagrangian where (k>0) and we

For the two body central-force problem with a Newtonian potential, the effective two-dimensional orbit dynamics can be described by the Lagrangian

*+*^ + ($+8) m = + (2 + ) * = 7

where \(k>0\) and we have chosen to use Cartesian coordinates.

(a) Show that the equations of motion become

L

*+*^ + ($+8) m = + (2 + ) * = 7 L

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