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.

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

References in corpus (3)

• A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems
• The Kustaanheimo-Stiefel transformation in geometric algebra
• Energy levels of periodic solutions of the circular 2+2 Sitnikov problem