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首页> 外文期刊>Journal of applied mathematics and mechanics >Analysis of the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame
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Analysis of the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame

机译：带有两自由度动力陀螺仪的卫星平衡误差的稳定性分析

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摘要

A method that enables a conclusion to be drawn regarding the nature of the Lyapunov stability of the equilibria positions of autonomous systems with partial dissipation from the nature of the secular stability and truncated equations of the linear approximation is developed based on the Barbashin-Krasovskii theorem. The method is used to investigate the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame in a circular orbit. For the case when the axis of the gyroscope frame is oriented parallel to one of the principal axes of inertia of the satellite, the nature of the Lyapunov stability of all the equilibria, with the exception of a few branching points, is determined. It is established that gyroscopic stabilization, which is possible when there is no dissipation in the axis of the frame for certain equilibria that are unstable in the secular sense, breaks down when dissipation occurs.
机译：基于Barbashin-Krasovskii定理，开发了一种方法，该方法可以得出关于自发性系统的平衡位置的Lyapunov稳定性的性质，其中的长期耗散来自长期稳定性和线性逼近的截断方程的部分耗散。该方法用于研究带有两自由度动力陀螺仪的卫星的平衡稳定性，该陀螺仪在圆形轨道的框架轴上有耗散。对于陀螺仪框架的轴平行于卫星惯性主轴之一的情况，确定了除少数分支点外所有平衡的李雅普诺夫稳定性的性质。可以确定的是，陀螺稳定作用会在发生耗散时失效，而陀螺稳定作用会在世俗意义上不稳定的某些平衡状态下在框架的轴上没有耗散时发生。

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