Hamilton's Principle

A variational principle stating that the actual time evolution of a mechanical system between two fixed times makes the action integral S[q] = ∫_{t1}^{t2} L(q, q̇, t) dt stationary (extremal), where L is the Lagrangian (kinetic energy minus potential energy); the stationary condition yields the Euler–Lagrange equations which are the system's equations of motion under the chosen generalized coordin