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Homework Statement
For a gauge function G(t,q) where
does
A quick question about the same function, wouldOh, so you're just talking about Lagrangian mechanics.
If [itex]G[/itex] is a function of [itex]q[/itex] and [itex]t[/itex], then you have:
[itex]\dot{G} = \frac{\partial G}{\partial q} \dot{q} + \frac{\partial G}{\partial t}[/itex]
So in that case, [itex]\frac{\partial \dot{G}}{\partial \dot{q}} = \frac{\partial G}{\partial q}[/itex]
Yes, if [itex]G[/itex] is only a function of [itex]q[/itex] and [itex]t[/itex].A quick question about the same function, wouldbe a true statement?
G is a function of q and t, (G(t,q) to be exact). Could you explain why you can change the order of the derivatives in this case?Yes, if [itex]G[/itex] is only a function of [itex]q[/itex] and [itex]t[/itex].
If you have a function [itex]X(t,q)[/itex]of [itex]q[/itex] and [itex]t[/itex], then [itex]\dot{X} = \frac{d}{dt} X = (\frac{\partial}{\partial t} + \frac{\partial}{\partial q} \frac{dq}{dt}) X = (\frac{\partial}{\partial t} + \frac{\partial}{\partial q} \dot{q}) X[/itex]G is a function of q and t, (G(t,q) to be exact). Could you explain why you can change the order of the derivatives in this case?