On instability of the equilibrium state of nonholonomic systems
We establish a criterion of instability for the equilibrium state of nonholonomic systems, in which gyroscopic forces may dominate over potential forces. We show that, similarly to the case of holonomic systems, the evident domination of gyroscopic forces over potential ones is not sufficient to ens...
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| Date: | 1999 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4622 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510772879163392 |
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| author | Sosnitskii, S. P. Сосницький, С. П. |
| author_facet | Sosnitskii, S. P. Сосницький, С. П. |
| author_sort | Sosnitskii, S. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:09:58Z |
| description | We establish a criterion of instability for the equilibrium state of nonholonomic systems, in which gyroscopic forces may dominate over potential forces. We show that, similarly to the case of holonomic systems, the evident domination of gyroscopic forces over potential ones is not sufficient to ensure the equilibrium stability of nonholonomic systems. |
| first_indexed | 2026-03-24T03:02:19Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4622 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:02:19Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f1/5b72730bece3c91b4bbc7cf2dcbfeef1.pdf |
| spelling | umjimathkievua-article-46222020-03-18T21:09:58Z On instability of the equilibrium state of nonholonomic systems Про нестійкість рівноваги неголоиомних систем Sosnitskii, S. P. Сосницький, С. П. We establish a criterion of instability for the equilibrium state of nonholonomic systems, in which gyroscopic forces may dominate over potential forces. We show that, similarly to the case of holonomic systems, the evident domination of gyroscopic forces over potential ones is not sufficient to ensure the equilibrium stability of nonholonomic systems. Встановлено критерій нестійкості рівноваги иеголономних систем, в яких гіроскопічні сили можуть домінувати над потенційними. Показано, що аналогічно до випадку голономиих систем явне домінування гіроскопічних сил над потенційними не є достатнім, щоб забезпечити стійкість рівноваги иеголономних систем. Institute of Mathematics, NAS of Ukraine 1999-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4622 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 3 (1999); 389–397 Український математичний журнал; Том 51 № 3 (1999); 389–397 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4622/5947 https://umj.imath.kiev.ua/index.php/umj/article/view/4622/5948 Copyright (c) 1999 Sosnitskii S. P. |
| spellingShingle | Sosnitskii, S. P. Сосницький, С. П. On instability of the equilibrium state of nonholonomic systems |
| title | On instability of the equilibrium state of nonholonomic systems |
| title_alt | Про нестійкість рівноваги неголоиомних систем |
| title_full | On instability of the equilibrium state of nonholonomic systems |
| title_fullStr | On instability of the equilibrium state of nonholonomic systems |
| title_full_unstemmed | On instability of the equilibrium state of nonholonomic systems |
| title_short | On instability of the equilibrium state of nonholonomic systems |
| title_sort | on instability of the equilibrium state of nonholonomic systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4622 |
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