Solving a modified Kepler potential using a rotating reference frame

[juardilag]

Homework Statement

Show that the motion of a particle in the field of potential:
$$V(r)=-\frac{k}{r}+\frac{h}{r^2},$$
is the same as the motion under the Kepler potential only when expressed as a function of a coordinate system in rotation or precession about the center of forces.

Relevant Equations

Orbit equation

I have tried to solve the problem through the use of a rotating reference frame, since I should have as a solution an orbit given by the Kepler potential, but I haven't come up with anything. Any ideas ?

 

[berkeman]

Welcome to PF.

Can you show us what you have tried so far? We need to see your work before we can offer tutorial help. Also, when you start posting math equations, it's best if you can use LaTeX as described in the "LaTeX Guide" link in the lower left of the Edit window. Thanks.