High Quality Content by WIKIPEDIA articles! The basic principle of Lagrangian mechanics is that an object subjected to outside influences will "choose" a path which makes a certain quantity, the action, a minimum. The action is a functional, a mathematical relationship which takes an entire path and produces a single number. The physical path, that which the object actually follows, is the path for which the action is "stationary": any small variation of the path from the physical one does not significantly change the action. (Often, this is equivalent to saying the physical path is the one for which the action is a minimum.) Actions are typically written using Lagrangians, formulas which depend upon the object's state at a particular point in space and/or time. In non-relativistic mechanics, for example, a point particle's Lagrangian is the difference between kinetic and potential energy: L = K – U. The action, often written S, is then the integral of this quantity from a starting time to an ending time:

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