Thread: Lagrangian Mechanics

I was wondering if a path that minimises the action of a system is necessarily one which minimises the transit time of a particle in the system? Intuition has me thinking that the answer is yes, at least in the case i'm considering, but i don't really know how i would go about finding this for a general case.

I'm trying to come up with the alignments of an arbitrary number of chute segments so that the transit time of granular material is minimised. If minimising the action of the system is an equivalent formulation of the problem i thought maybe lagrangian mechanics could provide the appropriate equations i'm looking for.

Originally Posted by wallaby

I was wondering if a path that minimises the action of a system is necessarily one which minimises the transit time of a particle in the system? Intuition has me thinking that the answer is yes, at least in the case i'm considering, but i don't really know how i would go about finding this for a general case.

I'm trying to come up with the alignments of an arbitrary number of chute segments so that the transit time of granular material is minimised. If minimising the action of the system is an equivalent formulation of the problem i thought maybe lagrangian mechanics could provide the appropriate equations i'm looking for.

http://en.wikipedia.org/wiki/Cycloid