CERN Accelerating science

Preprint
Report number	MP-ARC-2003-547
Title	Basics of regularization theory
Author(s)	Celletti, A
Publication	2003
Imprint	2003
Number of pages	mult.
Subject category	Mathematical Physics and Mathematics
Abstract	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.