具有Poynting-Robertson阻力的广义光引力限制三体问题的非线性稳定性
Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
摘要：
本文讨论了带Poynting-Robertson阻力的广义光引力限制三体问题三角形平衡点的非线性稳定性。这个问题是广义的意义上说，较小的小学应该是一个扁球体。较大的一次波被认为是辐射波。我们已经进行了一阶和二阶归一化的问题的哈密顿量。我们应用KAM定理研究了非线性稳定性的条件。我们发现了三个临界质量比。最后，我们得出结论，三角形点是稳定的，在非线性意义下，除了三个临界质量比，KAM定理失败。
英文摘要：
The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.
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