In Lagrangian dynamics, when using the Lagrangian thus:
$$ \frac{d}{dt}(\frac{\partial \mathcal{L} }{\partial \dot{q_j}})- \frac{\partial \mathcal{L} }{\partial q_j} = 0 $$
often we get terms such as the one below which result in zero:
example 1: $$ \frac{\partial \dot{q}}{\partial q} = 0 $$ example 2: $$ \frac{\partial q}{\partial \dot{q}} = 0 $$
I wasn't sure why but this is the closest I have come to reasoning it out:
$$ \frac{\partial \dot{q}}{\partial q} = \frac{\partial \dot{q}}{\partial t}\frac{\partial t}{\partial q} = 0 $$
because
$$ \frac{\partial t}{\partial q} = 0 $$
and similar for example 2. Is this correct?
