Doubt in classical mechnaics

1. Aug 6, 2008

pardesi

is it necessarily true that we have
$$\frac{\partial T}{\partial q}=0$$?

2. Aug 6, 2008

Nick R

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. Aug 7, 2008

Andy Resnick

It's trivially not true for motion of one particle using polar coordinates (Goldstein, p. 26).

T=$\frac{1}{2}m (\dot{r}^{2} + (r\dot{\theta})^{2})$

4. Aug 8, 2008

pardesi

exactly that was my point of contradiction to my profs claim