Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem

Details Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem

2009-03-12

arxiv.org/abs/0903.2136v4

J. Phys. A: Math. Theor. 44 (2011) 265204

Physics

Mathematical Physics

23 pages, 5 figures. References to algorithmic regularization included, changes in References and small typographic correction

Scientific paper

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.

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