THE STUDY OF OSCILLATING DYNAMIC SYSTEMS IN THE CASE OF PARAMETRICAL PERTURBATION

Abstract

The dynamic systems study in this paper is from the category of the parametric oscillatory system .This cases appear when in the dynamic systems interfere modification in time of mechanical parameter (constitutive or geometrical) ;the variation of the elastic rigidity , the density variation , the variation of moment of inertia by modification of the centre of weight , of the length of the pendulum , of position and shape of same masses. This systems have a great practical utility in the case of cranes ,elevators or transporter on vibration base ,mechanisms with wells gears, the robotic of control and measurement devices. The study of these systems is made in a way of stability and control for optimizing and for evading catastrophe. In this paper is made a study of a dynamic nonlinear systems in a case of two oscillating masses tie nonstationary so: it is thought that a oscillator about m (mass) , (in general on a inclined plane ) which from is suspend it a pendulum m and length l(t) of a wire (crane) , LaGrange equation leading to nonlinear systems which are solve by successive approximate or by equation of Mathieu tip for which is study stability with Aince-Strutt diagrams.