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## Main Question or Discussion Point

In Lagrangian mechanics, can anyone show how to find the extrema of he action functional if you have more constraints than degrees of freedom (for example if the constraints are nonholonomic) using Lagrange Multipliers?

I've looked everywhere for this (books, papers, websites etc.) but none of them use the Calc. of Variations approach, they simply say something like "well assume a multiplier exists that makes this term zero" and go from there. I've never seen this derived from Hamilton's principle, which is what I think this is all about. I'll bet Lagrange looked at the problem in terms of finding a stationary point of a function, then applied the same idea to functionals. I'd like to see how this works, so I'd appreciate if someone could show me.

Thanks

I've looked everywhere for this (books, papers, websites etc.) but none of them use the Calc. of Variations approach, they simply say something like "well assume a multiplier exists that makes this term zero" and go from there. I've never seen this derived from Hamilton's principle, which is what I think this is all about. I'll bet Lagrange looked at the problem in terms of finding a stationary point of a function, then applied the same idea to functionals. I'd like to see how this works, so I'd appreciate if someone could show me.

Thanks