Quatro aplicações da álgebra linear na engenharia

Abstract

This work is mainly directed to Engineering students and has like main focus to present applications of Linear Algebra in this field, with the purpose of motivating Engineering graduates, relating the theory with the reality of the problems that will certainly face in the exercise of their professional activities. In this context, four applications are presented. The first one deals with basic electrical circuits, where it is shown that it is possible to determine the voltages and electrical currents of a circuit by solving a linear system, basic content of the Linear Algebra discipline. The second application uses the concepts in linear transformations to determine the positioning of a robotic arm in the plane and that, for this purpose, it is necessary to use composition of rotational and translational matrices in defined axes. The third application involves systems of first order linear equations to describe the equations of position and velocity of a system of a spring attached to a wall with a particle of mass m at its end. To get such equations it was not considered presence of friction and other external forces. Using Newton Second Law with Hooke Law for the spring, it was possible to arrive at a second order linear equation for the positioning of the particle and then it was possible to solve the problem by means of a system of first order equations which have provided , simultaneously, equations of velocity and displacement of the spring system. As a consequence of the sinusoidal nature of the solution found, the mechanical system of the spring is known as a simple harmonic oscillator. The fourth application, still related to systems of linear equations of the first order, deals with the displacement of the floors of a building because an earthquake. For that, a problem was used involving an earthquake and its impact on a n floors building, using concepts of Newtonian Mechanics, like Newton's Second Law and Hooke's Law. For Mathematical Modeling, it was used as basis a system of n second order differential equations, where each system equation's describes / models the effect of the seismic shock on the nth floor of a building.