skip to main content

SciTech ConnectSciTech Connect

Title: Topological classification of systems of Kovalevskaya-Yehia type

All the Fomenko-Zieschang invariants are calculated for the Kovalevskaya-Yehia problem, for all noncritical values of the parameters g and λ, by constructing admissible systems of coordinates and determining the mutual disposition of the basis cycles. The family of Kovalevskaya-Yehia systems contains 29 pairwise Liouville non-equivalent foliations. These foliations include those that are equivalent to previously known foliations, which arose in the integrable cases of Kovalevskaya and of Kovalevskaya-Yehia for g = 0, in the Zhukovskiı case, and in the Goryachev-Chaplygin-Sretenskiı case. Eleven new foliations are included in the 29 foliations, new in the sense that they are not Liouville equivalent to any foliations discovered earlier which arose in the known integrable cases of the rigid body. The topological type of the Liouville foliation for the family of Kovalevskaya-Yehia systems stabilizes at large values of the energy H, and this 'high-energy' system is roughly Liouville equivalent, at one of the energy levels, to the Goryachev-Chaplygin-Sretenskiı integrable case, which is already known. Bibliography: 29 titles.
Authors:
 [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22365787
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CLASSIFICATION; COORDINATES; ENERGY LEVELS; ENERGY SYSTEMS; INTEGRAL CALCULUS; INVARIANCE PRINCIPLES; MATHEMATICAL SOLUTIONS; TOPOLOGY