- #1

logic smogic

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**Problem**

A particle moves in a force field described by

[tex]F(r)=-\frac{k}{r^{2}}e^{-\frac{r}{a}}[/tex]

where k and a are positive.

Write the equations of motion and reduce them to the equivalent one-dimensional problem. Use the effective potential to discuss the qualitative nature of the orbits for different values of the energy and the angular momentum.

**Attempt at Solution**

I'm having trouble deriving the potential V. Given the force equation F(r), we should have

[tex]F(r)=-\nabla V[/tex]

Since the Lagrangian L is defined as [tex]L=T-V[/tex], we need to know the potential V. We can derive this by integrating the force equation. But I've searched through many integral tables, and come across nothing for this particular integrand!

Can anyone help with this simple step?