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періодичних видань НАН України
періодичних видань НАН України
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
Інший ID:
2010 Mathematics Subject Classification: 37N15; 70E15; 70H33; 74A99
DOI:10.3842/SIGMA.2010.031
DOI:10.3842/SIGMA.2010.031
Посилання:
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints / V. Kovalchuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 18 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Eighth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2009.html.
ts
This paper contains results obtained within the framework of the research project 501 018
32/1992 financed from the Scientific Research Support Fund in 2007–2010. The author is
greatly indebted to the Ministry of Science and Higher Education for this financial support.
The author is also very grateful to the referees for their valuable remarks and comments
concerning this article and some propositions of the further investigation of the subject.
Дата:
2010
Переглядів:
468
Завантажень:
248
Анотація:
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff-Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it simultaneously performs one-dimensional oscillations orthogonal to this central plane. For the polar decomposition we obtain the stationary ellipsoids as special solutions of the general, strongly nonlinear equations of motion. It is also shown that these solutions are conceptually different from those obtained earlier for the two-polar (singular value) decomposition.
