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Regularization of simultaneous binary collisions in the n-body problem

✍ Scribed by Carles Simó; Ernesto A Lacomba

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
877 KB
Volume
98
Category
Article
ISSN
0022-0396

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1. We show that in the collinear \(N\)-body problem any simultaneous binary collision singularity ( \(\mathrm{SBC}\) ) of \(L\) pairs of particles, with no other collisions, is \(C^{l}\) blockregularizable, that is, we show that near such an orbit there is a \(C^{1}\) diffeomorphism from collision a

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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 t