论文标题
科伦坡最高问题的分析解决方案
Analytical solution of the Colombo top problem
论文作者
论文摘要
科伦坡顶部是在旋转动力学上的基本模型，该天体在进攻轨道上移动并被重力扭矩扰动。本文介绍了针对此问题的分析解决方案的详细研究。通过求解4度的代数方程，我们为其能量的函数提供了极端轨迹点的表达。固定点的位置（称为Cassini状态）被发现是问题的两个参数的函数。分析解决方案用weierstrass和jacobi椭圆函数用于常规轨迹。某些轨迹通过基本功能表达出来：不仅是预期的，不仅是同型轨道轨道，而且是一种特殊的周期溶液，其能量等于第一个Cassini态的能量（在先前的研究中未注意）。
The Colombo top is a basic model in the rotation dynamics of a celestial body moving on a precessing orbit and perturbed by a gravitational torque. The paper presents a detailed study of analytical solution to this problem. By solving algebraic equations of degree 4, we provide the expressions for the extreme points of trajectories as functions of their energy. The location of stationary points (known as the Cassini states) is found as the function of the two parameters of the problem. Analytical solution in terms the Weierstrass and the Jacobi elliptic functions is given for regular trajectories. Some trajectories are expressible through elementary functions: not only the homoclinic orbits, as expected, but also a special periodic solution whose energy is equal to that of the first Cassini state (unnoticed in previous studies).
