Abstract

Using the software developed on the basis of the computer algebra system Mathematica, we study the rotational motion along the circular orbit of a satellite-gyrostat in a Newtonian central field of forces. The linearized equations of a perturbed motion in the vicinity of the relative equilibrium of the system are constructed on a computer in symbolic form, and the necessary stability conditions are obtained for the equilibrium. Implementing the parametric analysis of the derived inequalities, we consider one of the cases when the vector of the gyrostatic moment of the system lies in one of the planes formed by the principal central axes of inertia. The obtained stability regions have an analytical form or a graphical representation as 2D images.

中文翻译：

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轨道陀螺仪相对平衡必要稳定性条件的符号-数值分析

摘要

使用在计算机代数系统Mathematica的基础上开发的软件，我们研究了牛顿中心力场中沿卫星陀螺仪的圆形轨道的旋转运动。在计算机上以符号形式构造系统相对平衡附近的摄动运动的线性方程，并为该平衡获得必要的稳定性条件。在对导出的不等式进行参数分析时，我们考虑系统回旋矩矢量位于主惯性中心轴形成的平面之一中的情况之一。所获得的稳定性区域具有分析形式或作为2D图像的图形表示。