- #1

- 4

- 0

I'm trying to follow Goldstein textbook to show that the Lagrangian is invariant under coordinate transformation. I got confused by the step below

So

## L = L(q_{i}(s_{j},\dot s_{j},t),\dot q_{i}(s_{j},\dot s_{j},t),t)##

The book shows that ##\dot q_{i} = \frac {\partial q_{i}}{\partial s_{j}} \dot s_{j} + \frac{\partial q_{i}}{\partial t} ##,and I'm not sure where the ##\frac{\partial q_{i}}{\partial t} ## term come from? I've tried to look up chain rules for coordinate transformation but I can't find anything.

Please help!

Thank you :D