Recent content by pccrp

But why in dynamic situations only the sum must be zero, and not each member of the sum?

/I'm having some doubt with D'alembert's Principle. The principle states that \sum_{i}(\vec {F}_i - \dot{\vec{p}}_i)\delta\vec{r}_i=0 but does that mean that each term of the summation must vanish too, or just the sum does? I know that mathematically there's no need that each term shall vanish...

Think I got it now. \dot{q} is not a function of q, it's only a function of the variable t. Being so, if we partially derivate L(q,\dot{q},t) w.r.t to \epsilon we know that the partial derivatives w.r.t. to q(i.e.\frac{\partial L}{\partial q}) will "see \dot{q} as constants" and vice versa, just...

Thanks a lot. My only question now is: How can we prove that we can apply the chain rule over the L(q,\dot{q},t) the same way we would if q and \dot{q} were not related to each other at all? Furthermore, if you find any demonstration of the general chain rule, it would also be very nice...

Adapting my thoughts, the terms \frac{\partial L}{\partial q_j} and \frac{\partial L}{\partial \dot q_j} (where the \frac{\partial L}{\partial q_j} treats \dot q_j as constants and vice versa) appear in the Lagrangian equations of motion because when proving the from Hamilton's principle, the...

Gathering answers around books and counting on all your greatly helpful answers (thanks, by the way), I successfully got to a conclusion and I would really appreciate if you could say to me if that's true or not. In my head, it's just a mathematical reason that you can consider them as...

I understand they're all needed to specify the state of the system. However, how can you start from this and prove the equations?

Hello! I've read thousand of explanations about how q and q-dot are considered independent in the Lagrangian treatment of mechanics but I just can't get it. I would really appreciate if someone could explain how is this so and (I've seen something about an a-priori independence but I couldn't...