THE EQUATIONS OF THE MOVEMENT OF THE SPHERICAL PENDULUM THROUGH THE LAGRANGIAL MECHANICS

Abstract

Newtonian Mechanics, formulated by Isaac Newton, was, until the mid-eighteenth century, the best tool available for studying dynamical problems. However, this required more coordinates to work than necessary. The study carried out by Lagrange, at the end of the 18th century, aimed to make the method of obtaining the equations of motion of natural phenomena established in the social and scientific sphere more simple and elegant. This was done through d'Alembert's Principle and the introduction of generalized coordinates in Analytical Mechanics. Unlike Newtonian Mechanics, Lagrangian Mechanics eliminates any reference to bonding forces, which brings us great advantage, since in most cases we do not immediately know the expressions that define bonding forces. The objective of this text is to present, in a simple and concise way, the lagrangian mechanics and to show the equations of the spherical pendulum's motion.

DOI: https://doi.org/10.56238/edimpacto2025.089-007