arXiv subjects

E. Lacomba

Publications and source records attributed to E. Lacomba.

3 recordsLinked to original sources

arXiv2011

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

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.

math-ph↗

arXiv2010

Energy levels of periodic solutions of the circular 2+2 Sitnikov problem

We study a 2+2 body problem introduced in a previous paper as the circular double Sitnikov problem. Since the secondary bodies are moving on the same perpendicular line where evolve the primaries, almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits and their foliations .

math-ph↗

arXiv2009

On the periodic orbits of the circular double Sitnikov problem

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries evolve, so almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits.

math-ph↗