I am working through the derivation of the lagrangian but don't get this step:

\(\displaystyle \frac{\partial T}{\partial \dot{q}}=\sum_{i=1}^N m_i \mathbf{\dot{r}}_i \cdot \frac{\partial \mathbf{\dot{r}_i}}{\partial \dot{q}} =\sum_{i=1}^N m_i \mathbf{\dot{r}}_i \cdot \frac{\partial \mathbf{r}_i}{\partial q}\)

T is the kinetic energy initially specified in terms of rectangular cartesian co-ordinate variables r_i and then generalised to general co-ordinates q_i. In this step why is d r_dot / d q_dot = d r / d q?

\(\displaystyle \frac{\partial T}{\partial \dot{q}}=\sum_{i=1}^N m_i \mathbf{\dot{r}}_i \cdot \frac{\partial \mathbf{\dot{r}_i}}{\partial \dot{q}} =\sum_{i=1}^N m_i \mathbf{\dot{r}}_i \cdot \frac{\partial \mathbf{r}_i}{\partial q}\)

T is the kinetic energy initially specified in terms of rectangular cartesian co-ordinate variables r_i and then generalised to general co-ordinates q_i. In this step why is d r_dot / d q_dot = d r / d q?

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