Cálculo variacional e a dinâmica lagrangiana: uma aplicação usando o GeoGebra.

Abstract

This work presents an application of Variational Calculus with Lagrangian Dynamics using GeoGebra software. Lagrangian dynamics is linked to variational calculus in the deductions of the equations of motion of dynamical systems. For that, a theoretical approach of the two themes is presented and then two dynamic systems are studied, the pendulum car without external forces and the inverted pendulum car. The equations of motion of these systems are nonlinear differential equations, which need a numerical method to solve. GeoGebra is a dynamic mathematical software that brings together many features, including solving nonlinear differential equations and building dynamic activities. That said, in this work GeoGebra is used to solve the equations of motion of the pendulum car systems without external forces and the inverted pendulum car, and the construction of two interactive activities of these systems made in GeoGebra, the applets, is also presented. In addition, some simulations performed in the animations are presented, in order to illustrate and visualize the behavior of the system, as well as validating these constructs. In this work it is shown that GeoGebra numerically solves nonlinear differential equations, still allowing animated visualization of the solution