The Principle of Least Action posits that the trajectory followed by a mechanical system between two states is the one that minimizes (or makes stationary) the action integral, defined as the time integral of the Lagrangian function. This variational principle provides an alternative to Newton's laws for deriving equations of motion using scalar quantities rather than vector forces, forming a foundational pillar within analytical mechanics and classical field theory. The formalism relies on precise definitions of generalized coordinates, constraints, and boundary conditions to establish a rigorous framework applicable across continuous physical systems without reference to specific force vectors.
Prerequisite chain context: requires Lagrangian Formulation of Mechanics for Single Particles.