- #1

- 10

- 0

I'm trying to understand something about the lagrangian.

My resources for learning a currently limited to Landau's mechanics and anything which is on the internet.

[tex] L = L(q,\dot{q},t) [/tex]

Now, here is a simple question: what are these generalized co-ordinated exactly?

For example, in Landau, does the "component-wise" lagrangian as such:

[tex] \frac{d}{dt} \frac{\partial L}{\partial \dot{q}_i } -

\frac{\partial L}{\partial{q_i}} = 0[/tex]

and several pages later he says:

[tex] \frac{d}{dt} \frac{\partial L}{\partial \vec{v} } [/tex]

but in general, the [tex] i^{\mbox{th}} [/tex] component of [tex]\vec{v}[/tex] isn't equal to the time derivative of [tex] q_i [/tex].

So what is it? [tex] \dot{q_i} \neq \frac{dq_i}{dt} [/tex] ??

Could someone recommend some books which would better explain this stuff?

Thanks,

Amir