# Energy and Derivatives

1. Sep 17, 2008

### Winzer

1. The problem statement, all variables and given/known data
Prove:
Even derivatives conserve energy and that odd derivatives give an energy loss.

This is for general forces acting on a system of some sort. Like drag force, etc.

2. Relevant equations

3. The attempt at a solution
I have no clue. I need resources. Any clues on where to begin?

2. Sep 18, 2008

### bdforbes

Is there any other context given for this problem? It seems a bit vague. What are these derivatives with respect to?

3. Sep 18, 2008

### Winzer

The derivatives are rates of displacement. Taken with respect to time.
An example is:
$$\vec{F}=-b \frac{dx}{dt}$$ The force of drag on a particle creates an energy loss in the system.

4. Sep 18, 2008

### bdforbes

I can't think of how to prove it formally but it will probably involve looking potential energy and closed loop integrations, are you familiar with those concepts?