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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, Number 3, Pages 34–43 (Mi vmumm31)  

Mechanics

A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: The equations of motion for a dynamically symmetric $n$-dimensional fixed rigid body-pendulum situated in a nonconservative force field are studied. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of an incident medium. The complete list of (in general) transcendental first integrals expressed in terms of a finite combination of elementary functions is found.

Key words: multi-dimensional rigid body-pendulum, dynamic equations, integrability, transcendental first integral.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00020-


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English version:
Moscow University Mechanics Bulletin, 2018, 73:3, 51–59

Bibliographic databases:

Document Type: Article
UDC: 517.01+531.01
Received: 11.11.2015

Citation: M. V. Shamolin, “A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 3, 34–43; Moscow University Mechanics Bulletin, 73:3 (2018), 51–59

Citation in format AMSBIB
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\paper A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere
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\issue 3
\pages 34--43
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\jour Moscow University Mechanics Bulletin
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\vol 73
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\pages 51--59
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