Saturday, 10 August 2013

Does $\frac{\partial \dot{r}}{\partial \dot{q}}=\frac{\partial r}{\partial q}?$

Does $\frac{\partial \dot{r}}{\partial \dot{q}}=\frac{\partial r}{\partial
q}?$

Would it considered abuse of notation to say something in the grounds of
$$\frac{\partial \dot{r_i}}{\partial \dot{q_j}}=\frac{\partial
r_i}{\partial q_j}?$$
It is supposed to follow from $$\dot{r_i}=\sum\limits_{k}\frac{\partial
r_j}{\partial q_k}\dot{q_k}+\frac{\partial r_i}{\partial t}.$$
But I can't see it.

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