Principle of Least Action, Hamilton’s PrincipleThe physical system moves along a path that minimizes or maximizes a certain quantity called action.Action is defined by 시간에 따른 시스템의 상태를 기술하는 Lagrangian 또는 HamiltonianStationary Action PrincipleEuler–Lagrange equation Hamilton's principleIn physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, the Lagrangian, which may contain all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the differential equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and plays an important role in quantum mechanics, quantum field theory and criticality theories.https://en.wikipedia.org/wiki/Hamilton's_principleAction principlesAction principles lie at the heart of fundamental physics, from classical mechanics through quantum mechanics, particle physics, and general relativity.[1] Action principles start with an energy function called a Lagrangian describing the physical system. The accumulated value of this energy function between two states of the system is called the action. Action principles apply the calculus of variation to the action. The action depends on the energy function and the energy function depends on the position, motion, and interactions in the system: variation of the action allows the derivation of the equations of motion without vector or forces.https://en.wikipedia.org/wiki/Action_principles