A REINTERPRETATION OF THE FLOQUET SOLUTION OF THE ORDINARY DIFFERENTIAL EQUATION SYSTEM WITH PERIODIC COEFFICIENTS AS A PROBLEM OF AN INFINITE MATRIX

Abstract

This paper presents an approach which transforms the problem of finding the general solutions of linear ordinary differential equation systems with periodic coefficients in eigenvalue and eigenvector problems of an infinite matrix. The problem of determining particular integrals for almost periodic input functions is also presented. This is equivalent to a problem of solving infinite linear algebraic equations. The paper includes an example application of the approach to the analysis of a simple electromechanical system. Results of numerical tests are also given.