Symplectic regularization of binary collisions in the circular N+2 Sitnikov problem

Hugo Jiménez-Pérez (1) , Ernesto A Lacomba (2)

1 OBSPM - Observatoire de Paris - Site de Meudon
2 Dept. of Math.

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 restricted circular N +2 body problem.

Mots clés: Physical Sciences

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Hugo Jiménez-Pérez, Ernesto A Lacomba. Symplectic regularization of binary collisions in the circular N+2 Sitnikov problem. Journal of Physics A: Mathematical and Theoretical, 2011, 44 (26), pp.265204. ⟨10.1088/1751-8113/44/26/265204⟩. ⟨hal-00839852⟩