In lagrangian mechanics Is the path that take a System in the configuration space between initial and final state is identical to the geodesic which connect the two points?
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$\begingroup$ Essentially a duplicate of Can Lagrangian be thought of as a metric? $\endgroup$– Qmechanic ♦Commented Feb 6, 2022 at 11:13
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I think this will depend upon the details of the actual action. In many common cases it will be.
Moreover, we require the configuration manifold to be at least a pseudo-Riemannian manifold in order to even define the notion of a geodesic.
answered Feb 6, 2022 at 11:08