On a parametric stability identification method with applications

Abstract

The research is focused on the theoretical study of the Lyapunov stability of the evolution of a dynamical system depending on parameters. It is described an original method of separation between the stable and unstable zones, in the plane of chosen principal parameters. In the paper is presented, using this results, an original method for identification, in the plane of principal parameters of the mathematical model of the dynamical system, the stable and unstable regions of the motion. We analyze also some theorems, as the Floquet stability theorem, concerning the stability of a dynamical system described by differential equation systems with periodical coefficients. The results are applied to the study of the couple pantograph – contact wire of a electrical locomotive. The parameters of the system are the two concentrated masses, the bending stiffness, the wire tension, the viscous damping and the mass per unit length of the wire, the other damping coefficients and stiffness elements of the system and any constant speed specified in the model. We study the stable and unstable regions of the dynamical system motion using these parameters and our method of stability zones identification.