Classical mechanic transformation

1. Sep 9, 2015

Mateusz

Hello everyone, I have a little problem with some transformation.
I wonder how i can get that result. Can somebody explain it step by step?
The " ' " means derivative. Thank you for your time ;)

2. Sep 9, 2015

Geofleur

Try starting with a really simple case, like if you have just $x_1 = f_1(q_1,q_2)$ and $x_2 =f_2(q_1,q_2)$. You can work out each term in the resulting Lagrangian in this case and that may help you see how it works in general.

3. Sep 9, 2015

loops496

As Geofleur said start with the simplest but non trivial case, then step it up a little bit, you'll see the pattern right away and convince yourself of the general formula.

4. Sep 11, 2015