# Finding potential from force

1. Sep 6, 2006

### genius2687

A perticle moves in a plane under the influence of a force, acting toward a center of force, whose magnitude is

F= 1/r^2{1 - 1/c^2[(r')^2 - 2(r'')r]}

where r is the distance of the particle to the center of force. Find the generalized potential that will result in such a force, and from that the Lagrangian for the motion in a plane.

I have assumed that we can use F = -partial(V)/partial(r). Is there an easy way to do this problem?

I have tried integrating the second term (r')^2/r^2 by parts (You get this when you distribute the 1/r^2 factor in front). When I do this, I get two terms, one of which looks like 1/r*2(r'(dr') instead of something in the form of (....)dr.