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Symbolic-Analytic Methods for Studying Equilibrium Orientations of a Satellite on a Circular Orbit
Programming and Computer Software ( IF 0.7 ) Pub Date : 2021-04-16 , DOI: 10.1134/s0361768821020055
S. A. Gutnik , V. A. Sarychev

Abstract

This paper proposes two simple methods for determining equilibrium orientations of a satellite moving in a central Newtonian force field along a circular orbit under the action of the gravitational torque. The first method uses linear algebra approaches, while the second one employs computer algebra algorithms. The equilibrium orientations of the satellite in the orbital coordinate system for given values of principal central moments of inertia are determined by the roots of a system of nonlinear algebraic equations. To determine the equilibrium solutions, the system of algebraic equations is decomposed using linear algebra methods and algorithms for Gröbner basis construction. The equilibria of the satellite are determined by analyzing the real roots of the algebraic equations from the Gröbner bases constructed. Using the proposed approach, it is shown that the satellite with unequal principal central moments of inertia has 24 equilibrium orientations on a circular orbit.



中文翻译:

研究圆形轨道上卫星平衡方向的符号解析方法

摘要

本文提出了两种简单的方法,用于确定在重力作用下,沿圆形轨道在牛顿中心力场中沿圆形轨道运动的卫星的平衡方向。第一种方法使用线性代数方法,而第二种方法使用计算机代数算法。对于给定的主要中心惯性矩值,卫星在轨道坐标系中的平衡取向由非线性代数方程组的根确定。为了确定平衡解,使用线性代数方法和用于Gröbner基构建的算法分解代数方程组。通过分析所构造的Gröbner基的代数方程的实根来确定卫星的平衡。使用建议的方法,

更新日期:2021-04-16
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