Is \(\frac{\partial T}{\partial q} = 0\) Always True in Classical Mechanics?

[pardesi]

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

 

[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?

 

[Andy Resnick]

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

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

 

[pardesi]

exactly that was my point of contradiction to my profs claim