Abstract:

This paper shows a proposal for the teaching of mechanical systems (SM) modeled with systems of differential equations (SED) using the Mathematica package. The strategy considers four phases. In the first, simple SMS are analyzed, such as the simple pendulum system and the mass-spring system on a plane. The Lagrangian of each system is determined and the Euler-Lagrange equations are used to construct the equations of motion. A second alternative is to determine the Hamiltonian of each system and use the Hamilton equations. Subsequently, the obtained EDS are solved analytically. In the second phase, SED solution programs in Mathematica are constructed using classical numerical methods such as Euler, Runge-Kutta of fourth order (Rk4) and Runge-Kutta-Feldberg of order 4-5 (RKF45). The programs are tested with the examples from the previous phase. In the third phase, a set of programs is elaborated in order to determine the equations of movement of any system using the equations of Euler-Lagrange (Hamilton) from the Lagrangian (Hamiltonian) system. In the fourth phase, complex problems are solved, such as the movement of a particle over a cone, or the movement of planets in the solar system. The programs developed in phases 2 and 3 are used in order to obtain a numerical solution of these examples. Finally, interactive graphical interfaces are constructed for each proposed system, with which the studied physical phenomena are analyzed. As a result, engineering students who use and build graphical interfaces have improved their understanding of SED and its use in classical mechanics. In addition, they change their previous ideas about the scope of mechanics and SEDs, obtain greater confidence in their knowledge and can solve dynamic problems through the use of simple numerical techniques.

Keywords:

Mechanical Systems, Mathematica, Differential Equations, Hamiltonian, Lagrange Equations, Hamilton Equations.