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Groups of symmetries in the two‐body problem associated to Einstein's PN field
Author(s) -
Mioc V.
Publication year - 2003
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.200310084
Subject(s) - homogeneous space , diffeomorphism , physics , commutative property , hamiltonian (control theory) , mathematical physics , vector field , einstein , classical mechanics , polar coordinate system , pure mathematics , mathematics , geometry , mathematical optimization , mechanics
The two‐body problem associated to a spherical post‐Newtonian (PN) field with Einsteinian parameterization is revisited from the single standpoint of symmetries. The corresponding vector fields, in Hamiltonian and standard polar coordinates, or in collision‐blow‐up and infinity‐blow‐upMcGehee‐type coordinates, present symmetries that form diffeomorphic commutative groups endowed with a Boolean structure. The existence of such symmetries is of much help in understanding characteristics of the global flow, or in finding symmetric periodic orbits in more complex problems depending on a small parameter.