Principle of Least Action

A variational principle stating that the actual trajectory of a physical system between specified states makes the action — the time integral of the Lagrangian — stationary with respect to nearby variations of the path, typically yielding the equations of motion via the Euler–Lagrange equations.

A variational principle stating that the true trajectory of a physical system between fixed endpoints makes the action functional stationary (typically an extremum), leading to the Euler–Lagrange equations that determine the system's evolution.

A variational principle stating that the actual trajectory of a mechanical system between two fixed states in time makes the action functional S = ∫_{t1}^{t2} L(q, q̇, t) dt stationary (δS = 0), where L is the system's Lagrangian (typically kinetic minus potential energy); the stationarity condition yields the Euler–Lagrange equations and thus the system's equations of motion in classical mechanic