Hamilton’s principle

Hamilton's principle, also known as the principle of least action, is a fundamental concept in physics. It states that for a dynamic system, the path taken between two configurations with the same total energy is the one for which the "action" is minimized or maximized.12

Introduced by Sir William Rowan Hamilton, the Hamiltonian function expresses the rate of change in time of a dynamic physical system. It defines the system's total energy, which is the sum of its kinetic and potential energies. This principle is foundational in understanding how physical systems evolve and has been crucial in the development of modern physics, including quantum mechanics.13