FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 1, PAGES 249-263
A. V. Shchepetilov
Abstract
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The problem of two particles with central interaction on
simply connected surfaces of a constant curvature was considered.
Due to the absence in this case of the Galileo transformation,
it's reduction
to the one particle problem was carried out by Marsden--Weinstein method.
The classification of reduced dynamic systems was given. For two of them
the conditions of the global solution existence for
dynamic equations with attractive potentials were found.
The comparison of the structure of obtained
Hamiltonians with integrals of one particle problem
with Bertrand's potentials was carried out.
All articles are published in Russian.
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Last modified: April 11, 2000