Maupertuis's principle

In classical mechanics, Maupertuis's principle (named after Pierre Louis Maupertuis) states 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. Mathematical formulation Maupertuis's principle states that the true path of a system described by generalized coordinates between two specified states and is a stationary point (i.e., an extremum (minimum or maximum) or a saddle point) of the abbreviated action functional where are the conjugate momenta of the generalized coordinates, defined by the equation