Abstract

A nonstationary two-body problem is considered such that one of the bodies has a spherically symmetric density distribution and is central, while the other one is a satellite with axisymmetric dynamical structure, shape, and variable oblateness. Newton’s interaction force is characterized by an approximate expression of the force function up to the second harmonic. The body masses vary isotropically at different rates. Equations of motion of the satellite in a relative system of coordinates are derived. The problem is studied by the methods of perturbation theory. Equations of secular perturbations of the translational-rotational motion of the satellite in analogues of Delaunay–Andoyer osculating elements are deduced. All necessary symbolic computations are performed using the Wolfram Mathematica computer algebra system.

中文翻译：

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用计算机代数研究非平稳两体问题中平移-旋转运动的长期扰动

摘要

考虑了一个非平稳的两体问题，使得其中一个物体具有球形对称的密度分布并且位于中心，而另一个则是具有轴对称动态结构，形状和可变扁度的人造卫星。牛顿的相互作用力的特征在于直至二次谐波为止的力函数的近似表达式。体重以不同的速率各向同性地变化。推导了卫星在相对坐标系中的运动方程。这个问题是用摄动理论的方法研究的。推导了Delaunay–Andoyer振荡元素类似物中卫星的平移-旋转运动的长期扰动方程。使用Wolfram Mathematica计算机代数系统执行所有必要的符号计算。