Hamilton's principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action (see that article for historical formulations). It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains 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.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q1, q2, ..., qN) between two specified states q1 = q(t1) and q2 = q(t2) at two specified times t1 and t2 is a stationary point (a point where the variation is zero), of the action functional
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