Maupertuis' principle

In classical mechanics, Maupertuis' principle (named after Pierre Louis Maupertuis), is that the path followed by a physical system is the one of least length (with a suitable interpretation of path and length). It is a special case of the more generally stated principle of least action. Using the calculus of variations, it results in an integral equation formulation of the equations of motion for the system.

Maupertuis' principle states that the true path of a system described by ${\displaystyle N}$ generalized coordinates ${\displaystyle \mathbf {q} =\left(q_{1},q_{2},\ldots ,q_{N}\right)}$ between two specified states ${\displaystyle \mathbf {q} _{1}}$ and ${\displaystyle \mathbf {q} _{2}}$ is an extremum (i.e., a stationary point, a minimum, maximum or saddle point) of the abbreviated action functional

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