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Some regularization in the N ‐body problem
Author(s) -
Diacu F. N.
Publication year - 1987
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113080222
Subject(s) - collision , singularity , gravitational singularity , motion (physics) , physics , regularization (linguistics) , classical mechanics , infinity , euclidean geometry , mathematical analysis , mathematics , geometry , computer science , artificial intelligence , computer security
Abstract We consider the simultaneous collision of n bodies in the general N ‐body problem, 2 ≤ n ≤ N , in the k ‐dimensional Euclidian space and eliminate the singularities which arise from that collision in the equations of motion by suitable coordinates and time transformations. The singularity of that solution is removed by throwing the collision instant to infinity. The new equations of motion are therefore defined in the large and they give a better description of the motion near the collision.