Energy Conservation in a Central Force

For conservative central forces and a defined interaction potential, V(r), we can write a statement for the total mechanical energy for a particle of mass M, a distance r away from a central force F as 

In addition to the total energy equation given above, we also have the condition of conservation of angular momentum, 

The quantities E and are the constants of motion, while V(r) is the potential-energy for a particle of mass Min a central field. We rewrite (3.20) in the form 

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