Ordinary differential equations and transient analysis in electric circuits

• Grant number: 12/12294-6
• 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 Alves Martinez
• 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 on non-homogeneous linear differential ordinary equations (DOEs), with constant coefficients, having as part non homogeneous, functions with finite discontinuities. Many physics phenomena are modeled by equations of this nature, such as in mechanical vibrations, electric oscillations, molecular vibrations, etc. Some problems will be studied involving DOEs that modeling some physics phenomena in electric circuits, having functions with finite discontinuities representing voltage sources (impute voltage source of electric circuit), 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)