- #1

bobred

- 173

- 0

## Homework Statement

Find the equations of motion for both r and [itex]\theta[/itex] of

## Homework Equations

My problem is taking the derivative wrt time of

and

[itex]\dfrac{\partial\mathcal{L}}{\partial\dot{r}}=m \dot{r} \left( 1 + \left( \dfrac{\partial H}{\partial r}\right)^2 \right)[/itex]

## The Attempt at a Solution

So

I think this is correct. I have the solution to the second expression but I am unsure how it was found

[itex]

m \ddot{r} \left( 1 + \left( \dfrac{\partial H}{\partial r}\right)^2 \right) + 2 m \dot{r}^2 \dfrac{\partial H}{\partial r}\dfrac{\partial^2 H}{\partial r \partial t}

[/itex]

The first part of this expression is fine it is the second part I am unsure of.