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## Homework Statement

a particle of mass m moves on the orbit [itex] r= a cos(θ), a>0[/itex].

Find the force acting on the particle

## The Attempt at a Solution

I had this formula in my notebook:

[itex]U(r)= E-(L^2/2mr^2)(1+(1/r^2)(dr/dθ)^2)[/itex]

Using it I got [itex] U(r)=E-L^2a^2/2mr^4[/itex]

and [itex] F(r)=-dU/dr= (-5L^2a^2/2mr^5) \overline{r}[/itex]

I would really appreciate if someone could confirm my result. I can't find other way to solve it but something smells fishy. Thanks!

edit: I will detail it a bit more

This is how I got the result

[itex]dr/dθ=-a sen(θ)[/itex]

[itex](dr/dθ)^2= a^2 sen(θ)^2 = a^2(1-cos(θ)^2)=(a^2-r^2)[/itex], then I just plugged this on the formula I'v written.

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