Doubt in classical mechnaics

  • Thread starter pardesi
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  • #1
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is it necessarily true that we have
[tex]\frac{\partial T}{\partial q}=0[/tex]?
 

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  • #2
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I imagine kinetic energy often varies if a generalized coordinate of the system varies. I don't see why that derivative would be 0 in general.

For instance, if the generalized coordinate q describes the angular velocity of a body about some axis, and q varies while holding all other generalized coordinates constant, then the kinetic energy T of the system varies, and that derivative is non-0... right?
 
  • #3
Andy Resnick
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It's trivially not true for motion of one particle using polar coordinates (Goldstein, p. 26).

T=[itex]\frac{1}{2}m (\dot{r}^{2} + (r\dot{\theta})^{2})[/itex]
 
  • #4
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exactly that was my point of contradiction to my profs claim
 

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