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Abstract: We present a brief overview of the regularizing transformations of the Keplerproblem and we relate the Euler transformation with the symplectic structure ofthe phase space of the N-body problem. We show that any particular solution ofthe N-body problem where two bodies have rectilinear dynamics can beregularized by a linear symplectic transformation and the inclusion of theEuler transformation into the group of symplectic local diffeomorphisms overthe phase space. As an application we regularize a particular configuration ofthe circular N+2 Sitnikov problem.



Author: H. Jiménez-Pérez, E. Lacomba

Source: https://arxiv.org/



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