THE PRINCIPLE OF LEAST ACTION: AN INTRODUCTION

ABSTRACT

The principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. The principle can be used to derive Newtonian, Lagrangian, Hamiltonian equations of motion, and even General Relativity. It was historically called "least" because its solution requires finding the path that has the least change from nearby paths. Its classical mechanics and electromagnetic expressions are a consequence of quantum mechanics, but the stationary action method helped in the development of quantum mechanics.The principle remains central in modern physics and mathematics, being applied in the theory of relativity, quantum mechanics and quantum field theory, and a focus of modern mathematical investigation in Morse theory. Maupertuis’ principle and Hamilton’s principle exemplify the principle of stationary action.

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