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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, Number 2, Pages 25–30 (Mi vmumm132)  

Mechanics

Integrable systems in dynamics on a tangent foliation to a sphere

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: The mechanical systems which have the tangent bundle of a two-dimensional sphere as their phase space are studied. The potential nonconservative systems describing a geodesic flow are classified. A multi-parameter family of systems possessing the complete list of (in general) transcendental first integrals expressed in terms of finite combinations of elementary functions is found. Some examples from spatial dynamics of a rigid body interacting with a medium are given.

Key words: variable dissipation system, dynamic equations, integrability, transcendental first integral.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00848-а


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English version:
Moscow University Mechanics Bulletin, 2016, 71:2, 27–32

Bibliographic databases:

Document Type: Article
UDC: 531.01+531.552+517.925
Received: 12.05.2014

Citation: M. V. Shamolin, “Integrable systems in dynamics on a tangent foliation to a sphere”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 25–30; Moscow University Mechanics Bulletin, 71:2 (2016), 27–32

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