论文标题
统一双曲线和球形2体问题与生物品质
Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions
论文作者
论文摘要
球体和双曲线空间上的2体问题都是在复杂球上定义的全态哈密顿系统的真实形式。这在生物试验中接受了自然的描述，并使我们能够通过使其复杂化并将其视为球形系统的复杂化来解决有关双曲线系统的问题。这样，球体上的2体问题的结果很容易被翻译成双曲线病例。例如，我们实施了这一想法，以完全对双曲线3空间上的2体问题的相对平衡进行分类，从而具有严格的吸引力。
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions concerning the hyperbolic system by complexifying it and treating it as the complexification of a spherical system. In this way, results for the 2-body problem on the sphere are readily translated to the hyperbolic case. For instance, we implement this idea to completely classify the relative equilibria for the 2-body problem on hyperbolic 3-space for a strictly attractive potential.
