Understanding the Chain Rule in Euler-Lagrange Equations

[Lapidus]

In this document, how do I get 3.2 on page 12? I assume it is the Euler-Lagrange equation given in 3.1 just rewritten. But how?

Many thanks in advance

 

[Lapidus]

Any hints? I think in 3.1 they take the time derivative to get to 3.2. But I still can't see how that works out.

 

[dextercioby]

Well, then you need to go back to your calculus text and check the chain rule.

$$\frac{d}{dt} \frac{\partial L(q,\dot{q})}{\partial \dot{q}^{i}} =\frac{\partial^2 L}{\partial \dot{q}^{i} \partial q^{j}} \frac{dq^{j}}{dt} + ...$$