So the integral of the lagrangian over time must be stationary according to hamiltons principle.(adsbygoogle = window.adsbygoogle || []).push({});

One can show that this leads to the euler lagrange equations, one for each pair of coordinates (qi,qi').

But my book has now started on defining a generalized lagrangian where lagrangian multipliers are used to somehow extend the principle to holonomic constraint f(q1,...,qn) = 0.

My question is: Did the lagrangian not already work for holonomic constraints, if you took the displacements of the qi's to be independent? I should think so, so why is it that they want to start with these multipliers - are they trying to extend the lagrangian to work for systems in which you can use arbitrary displacements of the coordinates qi?

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# Homework Help: Lagrangian and principle of least action

Can you offer guidance or do you also need help?

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