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Doubt in classical mechnaics

  1. Aug 6, 2008 #1
    is it necessarily true that we have
    [tex]\frac{\partial T}{\partial q}=0[/tex]?
  2. jcsd
  3. Aug 6, 2008 #2
    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?
  4. Aug 7, 2008 #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]
  5. Aug 8, 2008 #4
    exactly that was my point of contradiction to my profs claim
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