二维轨道的三维研究
A three dimensional investigation of two dimensional orbits
摘要：
已知三轴势的主平面中的轨道倾向于垂直于这些平面的不稳定运动，因此即使它们是二维的，也需要对这些轨道进行三维研究。我们在这里提出了一个调查这样的轨道在众所周知的对数势，这表明，第三个维度必须考虑到研究时，他们和不稳定性的较小值的垂直于平面的力。部分混沌轨道存在于共振周围，但也存在于其他区域。垂直于平面的作用似乎与区分规则轨道和部分混沌轨道的隔离积分有关，但与区分部分混沌轨道和完全混沌轨道的积分无关。
英文摘要：
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here an investigation of such orbits in the well known logarithmic potential which shows that the third dimension must be taken into account when studying them and that the instability worsens for lower values of the forces normal to the plane. Partially chaotic orbits are present around resonances, but also in other regions. The action normal to the plane seems to be related to the isolating integral that distinguishes regular form partially chaotic orbits, but not to the integral that distinguishes partially from fully chaotic orbits.
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