- #1

mia705

- 3

- 0

## Homework Statement

Derive the expression for kinetic energy of a classical particle in spherical coordinates.

## Homework Equations

I believe the answer I am supposed to reach is:

[tex]T=\frac{1}{2} m (\dot{r}^2 + r^2\dot{\theta^2} + r^2\dot{\phi ^2}sin^2\theta)[/tex]

## The Attempt at a Solution

[tex]T=\frac{1}{2}mv^2[/tex]

[tex]T=\frac{1}{2}m(\dot{x^2} + \dot{y^2} + \dot{z^2})[/tex]

Knowing that:

[tex] x=rsin\theta cos\phi [/tex]

[tex] y=rsin\theta sin\phi [/tex]

[tex] z=rcos\theta[/tex]

After plugging these in and working it out, I came up with:

[tex] T= \frac{1}{2}mr^2 [/tex]

My question now is, how do I get from the answer that I currently have to the solution I am trying to get to (that I listed above in part 2)?