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Goldstein Problemby SeReNiTy
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#1
Sep1206, 01:05 AM

P: 171

Can someone point me in the right direction with the derivation number 2 from Chapter 2 (3rd edition) of Goldstein?



#2
Sep1206, 04:45 AM

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PF Gold
P: 4,982

Not everybody has the book unfortunately, but if you tell us what derivation it is then perhaps we can help.



#3
Sep1206, 06:06 AM

P: 171

The derivation is if the lagrangian contained velocity terms, derive what the conjugate momentum will be if the system is rotated by a angle in some direction.



#4
Sep1206, 11:17 AM

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P: 3,224

Goldstein Problem
I've got Goldstein, and I'm lost on that one too. (As on most of them, btw. )



#5
Sep1206, 08:41 PM

P: 171

How would you define a potential with velocity dependent terms?



#6
Sep1306, 07:23 AM

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PF Gold
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[tex] L=TV = \frac{1}{2} m (\dot{x}+\dot{y}+\dot{z})  V(x,y,z) [/tex] In cartesian coordinates. The conjugate momentum for a particular coordinate is given by: [tex] \frac{\partial L}{\partial \dot{x}}= p_x[/tex] Now if the system was rotated by a particular angle how would you then modify the original expression to deal with a rotation. If you consider the x,y,z coordinates to be a vector [tex]\mathbf{r}[/tex] rotated about any arbitrary unit vector [tex]\mathbf{\hat{a}}[/tex] by a small angle [tex]\theta[/tex]. Now all you have to do is findout how the x,y,z coordinates are related to [tex]\mathbf{\hat{a}}[/tex] through vector [tex]\mathbf{r}[/tex] and plug them into the lagrangian and see what the turn up. In some books they set [tex]\mathbf{\hat{a}}[/tex] parallel to the zaxis for ease of computation and normally call it [tex]\mathbf{\hat{k}}[/tex] instead. Like I say I don't have the textbook but I assume this is something to do with conservation of angular momentum? Need any more pointers just post. 


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