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?

$$\frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)$$

 

[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?

$$\frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)$$

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)