Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, Number 3, Pages 11–14 (Mi vmumm232)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: The paper presents the results of study of the motion equations for a dynamically symmetric 4D-rigid body placed in a certain non-conservative field of forces. The form of the field is taken from the dynamics of actual 2D- and 3D-rigid bodies interacting with the medium in the case when the system contains a non-conservative pair of forces forcing the center of mass of a body to move rectilinearly and uniformly. A new case of integrability is obtained for dynamic equations of body motion in a resisting medium filling a four-dimensional space under presence of a tracking force.

Key words: 4D-rigid body, dynamic equations, integrability in terms of transcendental functions.

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


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English version:
Moscow University Mathematics Bulletin, 2015, 70:3, 111–114

Bibliographic databases:

UDC: 517.925+531.01
Received: 28.03.2011
Revised: 23.09.2014

Citation: M. V. Shamolin, “New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 3, 11–14; Moscow University Mathematics Bulletin, 70:3 (2015), 111–114

Citation in format AMSBIB
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\paper New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2015
\issue 3
\pages 11--14
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\jour Moscow University Mathematics Bulletin
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\pages 111--114
\crossref{https://doi.org/10.3103/S002713221503002X}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Shamolin, “Integrable dynamical systems with dissipation on tangent bundles of 2D and 3D manifolds”, J. Math. Sci. (N. Y.), 244:2 (2020), 335–355  mathnet  crossref  elib
    2. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref
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