带偏心转子陀螺体的混沌运动

Chaotic Motion of Gyrostat with Mass - Eccentric Rotor

本文讨论无力矩条件下带有质量偏心轴对称转子的非对称陀螺体的运动。利用动量矩变量列写动力学方程,并将系统化作受周期微扰作用下的Euler-Poinsot运动。应用Melnikov方法预测系统存在Smale马蹄意义下的混沌运动。此结论与Poincar截面的数值计算相符。从Poincar截面的相图也可明显看出转子对于双自旋卫星的姿态稳定作用。

In this paper the motion of a torque - free asymmetric gyrostat with a mass - eccentric rotor is discussed. The dynamical equations are written with the variables of angular momentum. The system is reduced to an Euler -Poinsot motion perturbed by a small periodic excitation. The Melnikov function is calculated to predict the existence of chaotic motion. This result is verified by the numerical computation of the Poincare surfaces of section. The stabilizing effect of the rotor in the dual-spin satellite is also shown explicitly in the portrait of the Poincare surfaces of section