# least-action principle

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Related to least-action principle: Principle of least time, Hamilton principle, Principle of least privilege

## Least-action principle

Like Hamilton's principle, the principle of least action is a variational statement that forms a basis from which the equations of motion of a classical dynamical system may be deduced. Consider a mechanical system described by coordinates *q*_{1}, . . . , *q _{f}* and their canonically conjugate momenta

*p*

_{1}, …,

*p*. The action

_{f}*S*associated with a segment of the trajectory of the system is defined by the equation below,

*c*of the trajectory. The action is of interest only when the total energy

*E*is conserved. The principle of least action states that the trajectory of the system is that path which makes the value of

*S*stationary relative to nearby paths between the same configurations and for which the energy has the same constant value. The principle is misnamed, as only the stationary property is required. It is a minimum principle for sufficiently short but finite segments of the trajectory.

*See*Hamilton's equations of motion, Hamilton's principle, Minimal principles

## least-action principle

[¦lēst ′ak·shən ‚prin·sə·pəl] (mechanics)