Collision–Ejection Manifold and Collective Analytic Continuation of Simultaneous Binary Collisions in the PlanarN-Body Problem
✍ Scribed by Mohamed Sami ElBialy
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 256 KB
- Volume
- 203
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
We study simultaneous binary collision SBC singularities of L binaries in the planar N-body problem, 2 L F N. We introduce the generalized Levi-Civita transformation and follow it by a new transformation which we call the projective transformation near a SBC singularity. We use this transformation to show the following near a SBC singularity:
Ž . 1 In the generalized Levi-Civita variables, near a SBC singularity, the collection of collision and ejection orbits together with the singularity form a real Ž . analytic submanifold, which we call the collision᎐ejection CE manifold.
Ž . Ž . Ž . 2 Let R R R R be the collection of SBC SBE orbits in phase space, i.e,. in c e the original variables. Then, both R R and R R are real analytic.