Is the Lagrangian function invariant under coordinate transformations? If so, where can I find a proof?

Question

experimentx · Answer

the Lagrangian of a system depends only Difference of Kinetic energy and Potential Energy ... it is independent of choice of coordinates. It should remain invariant ... (i think ... i'm not expert on Lagrangian and Hamiltonian mechanics)

turingtest · Answer

check out at about 58min->rest of proof of this awesome lecture (the whole series is great) http://www.youtube.com/watch?v=3YARPNZrcIY&feature=BFa&list=SP189C0DCE90CB6D81

experimentx · Answer

ah .. Susskind

turingtest · Answer

yeah, he's just too cool

experimentx · Answer

let me master calculus first ...

turingtest · Answer

hehe, in the beginning of the series he has to give the students a calc I review because they apparently had forgotten it :)

experimentx · Answer

well ... i guess someday soon!!

experimentx · Answer

seems similar post http://www.physicsforums.com/showthread.php?t=118111

experimentx · Answer

sorry ... wrong post. it's for in-variance of la-grange's equation of motion ... i think it's called functional rather than function ... i never understood it

turingtest · Answer

Invarience under translation of coordinates is proven in what I just linked you too, but you should start from the first video and watch everything to really understand it

anonymous · Answer

Ok, I'll watch it and let you know. Thanks!