Um estudo da mecânica clássica sob as perspectivas de Newton, Lagrange e Hamilton

Abstract

Classical mechanics is a branch of physics that studies the dynamic behavior of physics systems using principles formulated by the English physicist Isaac Newton. Based on his observations and those of other scientists, Newton formulated three fundamental principles, or laws, for the study of mechanics. This article aims to present two formulations equivalent to Newton's , to achieve this, we will begin directly from the laws of motion, which describe the evolution of systems at each instant of time in Newtonian mechanics. Subsequently, we will address Lagrangian mechanics, using Hamilton's principle of least action to derive the equations of motion in the Lagrangian formalism, and then obtain Hamilton's canonical equations. With these equations which describe the system's dynamics in different formulations, we will apply these concepts to conservative systems, where the system's Hamiltonian is the total energy. Among the problems solved are the elastic pendulum, a particle in a spiral motion, a box sliding on a frictionless inclined plane, and a massive disk rolling down an inclined plane without sliding. Finally, the central idea is to derive the equations of motion for these different systems using the mechanics developed in this work and verify the advantages to simplicity to use one or others.