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Finding potential from force

  1. Sep 6, 2006 #1
    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.
     
  2. jcsd
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