Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem
Abstract
We present a brief overview of the regularizing transformations of the Kepler problem and we relate the Euler transformation with the symplectic structure of the phase space of the N-body problem. We show that any particular solution of the N-body problem where two bodies have rectilinear dynamics can be regularized by a linear symplectic transformation and the inclusion of the Euler transformation into the group of symplectic local diffeomorphisms over the phase space. As an application we regularize a particular configuration of the circular N+2 Sitnikov problem.
Keywords
Cite
@article{arxiv.0903.2136,
title = {Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem},
author = {H. Jiménez-Pérez and E. Lacomba},
journal= {arXiv preprint arXiv:0903.2136},
year = {2011}
}
Comments
23 pages, 5 figures. References to algorithmic regularization included, changes in References and small typographic corrections. Accepted in J. of Phys. A: Math. Theor 44 (2011) 265204 http://stacks.iop.org/1751-8121/44/265204