Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 2, Pages 3–12 (Mi vmumm129)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Chaplygin’s ball with a rotor: Non-degeneracy of singular points

A. I. Zhila

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (572 kB) Citations (1)
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Abstract: A problem of a dynamically balanced asymmetric ball with a rotor rolling over a rough horizontal plane is considered in the paper. Earlier, A. Y. Moskvin constructed bifurcation diagrams of the momentum map and bifurcation complexes in order to study the dynamics of the system and to obtain singular solutions. A natural development of this research is a fine Liouville analysis of the system. The first step in this direction is presented in the paper, namely, we verify the non-degeneracy of singularities and describe the Liouville foliation in a neighborhood of singular points of the momentum map.
Key words: Chaplygin ball with a rotor, conformally Hamiltonian systems, singular points of the momentum map, Liouville foliation, Fomenko–Zieschang invariants.
Received: 27.05.2015
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 2, Pages 45–54
DOI: https://doi.org/10.3103/S0027132216020017
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: A. I. Zhila, “Chaplygin’s ball with a rotor: Non-degeneracy of singular points”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 3–12; Moscow University Mathematics Bulletin, 71:2 (2016), 45–54
Citation in format AMSBIB
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  • This publication is cited in the following 1 articles:
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