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BASICS OF REGULARIZATION THEORY

机译:正则化理论的基础知识

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摘要

We consider the dynamics of three point masses, where we assume that the mass of the third body is so small that it does not affect the motion of the primaries. In the framework of the restricted three-body problem, we investigate the collisional trajectories, which correspond to a singularity of the equations of motion. We investigate the regularizing techniques known as Levi-Civita, Kustaanheimo-Stiefel and Birkhoff Transformations. The Levi-Civita regularization is adapted to the study of the planar restricted three-body problem, when considering a single collision with one of the primaries. The Kustaanheimo-Stiefel method concerns the same problem when the bodies are allowed to move in the 3-dimensional space. A simultaneous regularization with both primaries is achieved through the implementation of Birkhoff's transformation.
机译:我们考虑三点群众的动态,在那里我们假设第三身的质量如此之小,因此它不会影响原初的运动。在受限制的三体问题的框架中,我们研究了碰撞轨迹,该轨迹对应于运动方程的奇异性。我们调查了Levi-Civita,Kustaan​​heimo-Stiefel和Birkhoff变换的规律化技术。 Levi-Civita正规化适应平面限制的三体问题的研究,当时与其中一个初级碰撞时。 Kustaan​​heimo-Stieafel方法涉及当允许体在三维空间中移动时相同的问题。通过实现Birkhoff的转换来实现与两种重婚的同时正则化。

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