- #1
bobred
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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.