Abstract

Computer algebra and numerical methods were used to investigate the properties of a nonlinear algebraic system determining the equilibrium orientations of a system of two bodies connected by a spherical hinge that move in a circular orbit under the action of a gravitational torque. Primary attention was given to equilibrium orientations of the two-body system in the special cases when one of the principal axes of inertia of both the first and second body coincides with the normal to the orbital plane, the radius vector, or the tangent to the orbit. To determine the equilibrium orientations of the two-body system, the set of stationary algebraic equations of motion was decomposed into nine subsystems. The system of algebraic equations was solved by applying algorithms for constructing Gröbner bases. The equilibrium positions were determined by numerically analyzing the roots of the algebraic equations from the constructed Gröbner basis.

中文翻译：

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计算机代数方法在圆形轨道中两个相连物体系统的静止运动研究中的应用

摘要

计算机代数和数值方法用于研究非线性代数系统的性质，该系统确定由球状铰链连接的两个物体在重力作用下沿圆形轨道运动的系统的平衡方向。在特殊情况下，当第一和第二物体的惯性主轴之一与轨道平面的法线，半径矢量或与该物体的切线重合时，首先要注意两物体系统的平衡方向。轨道。为了确定两体系统的平衡方向，将一组固定的代数运动方程分解为9个子系统。代数方程组通过应用构造Gröbner基的算法求解。