Abstract

Methods of computer algebra are used to investigate equilibrium orientations of a satellite moving along a circular orbit under the action of gravitational and constant torques. The main focus is placed on the investigation of equilibrium orientations in the cases where the constant torque vector is parallel to the planes formed by the principal central axes of inertia of the satellite. Using methods for Gröbner basis construction, the system of six algebraic equations that determine the equilibrium orientations of the satellite is reduced to one sixth-order algebraic equation in one unknown. Domains with equal numbers of equilibrium solutions are classified using algebraic methods for constructing discriminant hypersurfaces. Bifurcation curves in the space of problem parameters, which define the boundaries of the domains with equal numbers of equilibrium solutions, are constructed. A comparative analysis of the influence of the order of variables in the process of Gröbner basis construction is carried out. Using the proposed approach, it is shown that, under the action of the constant torque, the satellite with unequal principal central moments of inertia has no more than 24 equilibrium orientations in a circular orbit.

中文翻译：

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用计算机代数方法研究恒扭矩对圆轨道卫星平衡方向的影响

摘要

计算机代数方法用于研究在重力和恒定扭矩作用下沿圆形轨道运动的卫星的平衡方向。主要重点研究恒扭矩矢量平行于卫星惯性中心轴形成的平面时的平衡方向。使用 Gröbner 基础构造方法，确定卫星平衡方向的六个代数方程组被简化为一个未知数的六阶代数方程。使用代数方法对具有相同数量平衡解的域进行分类，以构造判别超曲面。问题参数空间中的分岔曲线，构造了定义具有相同数量的平衡解的域的边界。对Gröbner基础构建过程中变量顺序的影响进行了对比分析。利用该方法表明，在恒力矩作用下，不等主中心转动惯量的卫星在圆形轨道上的平衡方位不超过24个。