Integral of force squared

1. Jun 13, 2009

maze

The path integral of force is the work, something that has a clear physical meaning we can relate to. My question is, what is the physical interpretation for the L2 norm of the force along a path? (integral of the force squared, basically):

$$\left(\int_\Gamma F \cdot F \right)^{\frac{1}{2}}$$

If a particle takes the path from point A to B which minimizes the work, then the least amount of external energy was expended moving it from point A to B. Can we analogously characterize the type of paths between 2 points that minimize the L2 norm of the force.

Thanks!

Last edited: Jun 13, 2009
2. Jun 13, 2009

gabbagabbahey

Do you mean:

$$\left(\int_\Gamma (\mathbf{F} \cdot \mathbf{F})ds \right)^{\frac{1}{2}}$$

?

3. Jun 13, 2009

maze

Yes, of course. F:R3->R3, $\Gamma:[0,1]->\textbf{R}^3$