Is there always a potential for conservative motion?

[Nusc]

Homework Statement

It is well known that for a conservative motion there is a potential.
This potential is a function of coordinates only.

Prove this.

Homework Equations

The Attempt at a Solution

I think you have to take a definition of conservative motion then for example prove that for such a motion, the rotational forces equals to 0 and they don't depend on time, then it will mean that there is a potential field.


What is the equation for conservative motion?

 

[Nusc]

I guess we suppose that the general form of the force field is F=F(q,p,t)

 

[NruJaC]

In general, a force is conservative iff the path integral of F around some closed path is equal to 0. This is equivalent to stating that the curl of F = 0.