- #1
Identity
- 152
- 0
Given an action:
[tex]S = \int L(q,\dot{q},t) \,dt[/tex]
The variation is:
[tex]\delta S = \int \left(\frac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial \dot{q}}\delta\dot{q}\right)\,dt[/tex]
I'm guessing this is some type of chain rule, but I haven't been able to derive it... how is it justified?
[tex]S = \int L(q,\dot{q},t) \,dt[/tex]
The variation is:
[tex]\delta S = \int \left(\frac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial \dot{q}}\delta\dot{q}\right)\,dt[/tex]
I'm guessing this is some type of chain rule, but I haven't been able to derive it... how is it justified?