The zonal satellite problem. III Symmetries | Zendy

Vasile Mioc | Zendy

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The zonal satellite problem. III Symmetries

Author(s) -

Vasile Mioc

Publication year - 2002

Publication title -

serbian astronomical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.196

H-Index - 16

eISSN - 1820-9289

pISSN - 1450-698X

DOI - 10.2298/saj0265001m

Subject(s) - homogeneous space , physics , commutative property , log polar coordinates , hamiltonian (control theory) , action angle coordinates , polar coordinate system , diffeomorphism , generalized coordinates , mathematical physics , pure mathematics , cartesian coordinate system , classical mechanics , geometry , mathematics , mathematical optimization

The two-body problem associated with a force field described by a potential of the form U =Sum(k=1,n) ak/rk (r = distance between particles, ak = real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita’s coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure

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