Consider the motion of a point mass m in the potential V(r)

[Muskovite]

Homework Statement

Consider the motion of a point mass m in the potential
V(r)=-k/r , k>0

Show that there is a solution x(t) of the equations of motion which is a circular motion
with constant circular frequency ω. Determine the relation between ω and the radius of the
circular motion. Show explicitely that energy and angular momentum are conserved along
the motion curve, by computing their values. Show also that the radius of the circular
motion coincides with the radius where the corresponding eective potential takes its
minimum.

Homework Equations

γ(t)=(rcos(ωt); r sin(wt)); r > 0; ω> 0;

The Attempt at a Solution

I am not really sure where to start. Maybe one can find the arc length for a piece of the curve γ, using this
s(t0,t1)=∫ from t0 to t1√(∑γ'k^2dx) and then go into the details, but for the moment I can't conjure up anything.
Any help would be highly appreciated.

 

[TSny]

It's hard to know what approach you are expected to use. Can you give us a little information about the concepts that you are currently studying that you feel are relevant to the question?

I don't understand your integral for the arc length. Can you explain how you arrived at the expression for the integrand and why you feel that an expression for arc length will help to solve the problem? Is the k in the integrand the same k that appears in the potential? Does your integrand have the right dimensions to represent length?