More derivative fun

  • Thread starter Ultimâ
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  • #1
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Main Question or Discussion Point

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?

[tex]
\frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)
[/tex]
 

Answers and Replies

  • #2
exk
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I would say product rule looks good.
 
  • #3
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Thanks for the input, will give it a go
 
  • #4
HallsofIvy
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Are you assuming here that [itex]\delta()/\delta[/itex] is a derivative? I would be more inclined to think it means "total variation".
 
  • #5
tiny-tim
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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?

[tex]
\frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)
[/tex]
Hi Ultimâ! :smile:

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

[tex]\frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)\,=\,-\dot{\theta} sin\theta[/tex] ? :confused:
 
  • #6
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It would be nice to think it was that simple tiny-tim, but I fear [tex] \dot{\theta}[/tex] is related to changes in [tex] \theta[/tex] 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)
 

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