Ordinary differential equations and electric circuits of second order

• Grant number: 12/12354-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2012
• End date: August 31, 2013
• Field of knowledge: Engineering - Electrical Engineering - Electrical, Magnetic and Electronic Circuits
• Principal Investigator: Francisco Villarreal Alvarado
• Grantee: Guilherme Santos Pereira
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

It is proposed to do a study of the principal classes of differential ordinary equations (DOEs). In particular, non homogeneous linear DOEs, with constant coefficients, will be studied, having as non homogeneous part the classical Dirac function (impulse function). Many physical phenomena of impulsive nature are modelled by equations of this type, such as in mechanical vibrations, electric oscillations, molecular vibrations, etc. Mechanical systems are frequently subject to actions of extern strength (or eletromotriz forces in the case of an electric circuit) of amplitude great that they act only for a short period of time. Some problems will be studied involving DOEs that model phenomena, principally, in electric circuits, having the Dirac function representing voltage sources (impute voltage source of electric circuit), resolved analytically and numerically and there will be done an analysis of the mathematical solution obtained taking into account the expectations of the real problem. For the analytical resolutions, of the considered DOEs, sequences of functions will be used, through approximation, as well as the techniques of the Laplace transformed, besides the use of the usual methods for resolution of DOEs. Also studies will be carried out of linear DOEs of second order that modeling vibratory systems mass-spring, considering three situations: non deadened free movement (harmonic simple movement), free deadened movement and forced movement (AU)