Simulación y análisis de un péndulo invertido acoplado a un resorte (PIAR)

Abstract

In this version, a qualitative study of an inverted pendulum coupled to a spring (PIAR) has been made based on their physical analysis and a simulation developed in Easy Java; this work is intended to serve as an educational resource for undergraduate students in physics who study subjects such as differential equations, vibrations and waves or introduction to computational physics. Among the various possible physical systems to study, the inverted pendulum represents a system of great interest because of its wide field of application. In robotics it is used to simulate the movement of the legs of the human being. In geophysics, instruments that measure the earth vibrations are known as seismometers; some designs of seismometers are based on the system composed of an inverted pendulum coupled to a spring. Given the change of its movement with respect to time and the possibility of presenting the linear to non-linear transition (analogous to the simple pendulum), PIAR is the system selected in this work to be studied from the qualitative theorem developed in Dynamical systems, always focused from a physical point of view. The situation, therefore, to be validated is: ¿How to teach the linear and non-linear transition of the inverted pendulum coupled to a spring from a physical point of view?