Interactive Mechanical Systems Using Mathematica

• Published in: Journal of physics. Conference series 2021-06, Vol.1936 (1), p.12017
• Main Authors: Santiago Acosta, R D, Hernández Cooper, E M, Hernández Medina, A, Gómez Castillo, R
• Format: Article
• Language: English
• Subjects: Classical mechanics; Conical bodies; Differential equations; Engineering education; Equations of motion; Euler-Lagrange equation; Graphical user interface; Interactive systems; Mass-spring systems; Mechanical systems; Numerical methods; Physics; Runge-Kutta method; Solar system
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1936/1/012017

This work shows a new proposal for teaching mechanical systems (SM) modelled through differential equations (SED) using the Mathematica package. The adopted strategy considers four stages. In the first, simple SMS, such as the mass-spring system on a plane or the simple pendulum, are analysed. The Lagrangian of each system is determined and the Euler-Lagrange equations are used to obtain the equations of motion. In other cases, the Hamiltonian of the systems is determined and the Hamilton equations are used. Afterwards, the resulting EDS are solved analytically. During the second stage, SED solution programs in Mathematica are developed by using classical numerical methods such as a fourth order Runge-Kutta method (Rk4) and a Runge-Kutta-Feldberg method of order 4-5 (RKF45). The programs are tested with the examples from the previous stage. In the next stage, a set of programs is elaborated in order to determine the equations of motion for any system by using the Euler-Lagrange equations (Hamilton) from the Lagrangian (Hamiltonian) of the system. In the last stage, complex problems such as the movement of planets in the solar system or the movement of a particle over a conical surface are solved. The programs developed during stages 2 and 3 are used in order to obtain a numerical solution to these examples. Finally, interactive graphical interfaces are constructed for each proposed system, and are used to study and analyse the physical phenomena. As a result, engineering students who use and build graphical interfaces have improved their understanding of SED and their use in classical mechanics. In addition, they change their previous ideas about the scope of mechanics and SEDs, they gain confidence in their knowledge and they are able to find solutions to dynamical systems through the use of simple numerical techniques.