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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 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

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.

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English version:
Moscow University Mathematics Bulletin, 2016, 71:2, 45–54

Bibliographic databases:

Document Type: Article
UDC: 511
Received: 27.05.2015

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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\vol 71
\issue 2
\pages 45--54
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Zhila, “Comparison of the system “Chaplygin ball with a rotor” and the Zhukovskii system from the rough Liouville equivalence point of view”, Moscow University Mathematics Bulletin, 72:6 (2017), 245–250  mathnet  crossref  mathscinet  isi
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