On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
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 t...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146341 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532414201397248 |
|---|---|
| author | Kovalchuk, V. |
| author_facet | Kovalchuk, V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2025-11-24T04:38:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146341 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:38:18Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kovalchuk, V. 2019-02-09T08:54:17Z 2019-02-09T08:54:17Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 37N15; 70E15; 70H33; 74A99 DOI:10.3842/SIGMA.2010.031 https://nasplib.isofts.kiev.ua/handle/123456789/146341 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints Article published earlier |
| spellingShingle | On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints Kovalchuk, V. |
| title | On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints |
| title_full | On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints |
| title_fullStr | On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints |
| title_full_unstemmed | On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints |
| title_short | On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints |
| title_sort | on classical dynamics of affinely-rigid bodies subject to the kirchhoff-love constraints |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146341 |
| work_keys_str_mv | AT kovalchukv onclassicaldynamicsofaffinelyrigidbodiessubjecttothekirchhoffloveconstraints |