Product Rule for Derivatives of Theta and Time Functions

[Ultimâ]

This is a bit weird, both are functions of theta (and time) ... so I assume the operator is on both ... is it a case of applying the product rule?

<br /> \frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)<br />

 

[exk]

I would say product rule looks good.

 

[Ultimâ]

Thanks for the input, will give it a go

 

[HallsofIvy]

Are you assuming here that \delta()/\delta is a derivative? I would be more inclined to think it means "total variation".

 

[tiny-tim]

This is a bit weird, both are functions of theta (and time) ... so I assume the operator is on both ... is it a case of applying the product rule?

<br /> \frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)<br />

Hi Ultimâ!

If this is calculus of variations, doesn't \frac{\delta}{\delta \theta} mean that you assume that \dot{\theta} is independent of \theta, so that:

\frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)\,=\,-\dot{\theta} sin\theta ?

 

[Ultimâ]

It would be nice to think it was that simple tiny-tim, but I fear \dot{\theta} is related to changes in \theta even for small variations. HallsofIvy, I'm not familiar with using the total variation approach, but it is part of a Jacobian so I would assume it was a derivative.

I've just posted the full problem here:
https://www.physicsforums.com/showthread.php?p=1731700#post1731700

(I know cross posting is frowned upon, but I was trying split the problem down into simpler components)