The least action principle

Abstract

In this article some historical aspects of the Principle of Least Action are introduced together with the mathematical methods and variational principles that allow this Principle to be implemented. This Principle carries implicit in its essence and structure, one of the most fundamental and profound ideas that have been established to understand nature. The central aspect of this Principle is the fact that to understand natural phenomena it is necessary to start from ideas related to simplicity, order, perfection and optimization of the resources available to nature to carry out its processes. In this article, the Principle of Least Action and the methods of calculus of variations are applied to physics, geometry and engineering. It is assumed that nature economizes all its processes and the human being, in engineering, in the design of structures and machines, seeks to imitate nature to optimize resources. Optimization methods in engineering are applied through mathematical models to determine maximum or minimum values ​​of certain variables or functions.