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## Homework Statement

The problem is to find the motion of a body in a central potential field with potential given by:

[tex]V(r)=-\frac{\alpha}{r}+\frac{\beta}{r^{2}}[/tex]

where [tex]\alpha[/tex] and [tex]\beta[/tex] are positive constants.

## Homework Equations

## The Attempt at a Solution

I used the fact that energy and angular momentum are conserved in this field, and after separating variables in the equation for [tex]\dot{\vec{r}}[/tex] I got an integral of the form: ([tex]\phi[/tex] is the angle)

[tex]\phi = \int{\frac{dr}{\sqrt{Ar^{3}-Br^{2}+C}}}[/tex]

where A, B, C are constants dependent on mass, energy and angular momentum of the body.

Is there a simpler method to find the motion [tex]r(\phi)[/tex], without having to calculate such awful integrals? And if not, how to calculate it?