High-Order Nonlinear Dynamics Systems for Artificial Satellites Orientation in Prolonged Reversal

Abstract

A problematic task is under consideration concerning the dynamics of orientation systems when their mathematical model is represented by high-order non-linear differential equations. In order to overcome difficulties confined with an accurate solution of such equations in a phase space a new method of reduction is suggested, which permits to turn the task into the investigation of motions on a two-dimensial multi-plate phase surface. The essense of the method is illustrated by an example of simplified system of third order. Some ways of searching complex motions and for determining their stability are suggested for a complete investigation of complex auto-vibrations arising in the system in question and being characteristic of a broad class of orientation systems.