Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives
We generalize the Ostrohrads'kyi method for the construction of the Hamiltonian description of a nondegenerate (regular) variational problem of arbitrary order to the case of degenerate (singular) Lagrangians. These Lagrangians are of major interest in the contemporary theory of elementary...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4323 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510455244521472 |
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| author | Nesterenko, V. V. Нестеренко, В. В. Нестеренко, В. В. |
| author_facet | Nesterenko, V. V. Нестеренко, В. В. Нестеренко, В. В. |
| author_sort | Nesterenko, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:26:41Z |
| description | We generalize the Ostrohrads'kyi method for the construction of the Hamiltonian description of a nondegenerate (regular) variational problem of arbitrary order to the case of degenerate (singular) Lagrangians. These Lagrangians are of major interest in the contemporary theory of elementary particles. For simplicity, we consider the Hamiltonization of a variational problem defined by a singular second-order Lagrangian. Generalizing the Ostrohrads'kyi method, we derive equations of motion in the phase space. We determine a complete collection of constraints of the theory. |
| first_indexed | 2026-03-24T02:57:16Z |
| format | Article |
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| id | umjimathkievua-article-4323 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:57:16Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/31/8b62f03b8f2a9e435882736e633d6d31.pdf |
| spelling | umjimathkievua-article-43232020-03-18T20:26:41Z Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives Формализм Остроградского для сингулярных лагранжианов с высшими производными Nesterenko, V. V. Нестеренко, В. В. Нестеренко, В. В. We generalize the Ostrohrads'kyi method for the construction of the Hamiltonian description of a nondegenerate (regular) variational problem of arbitrary order to the case of degenerate (singular) Lagrangians. These Lagrangians are of major interest in the contemporary theory of elementary particles. For simplicity, we consider the Hamiltonization of a variational problem defined by a singular second-order Lagrangian. Generalizing the Ostrohrads'kyi method, we derive equations of motion in the phase space. We determine a complete collection of constraints of the theory. Метод побудови гамільтонова опису для невиродженої (регулярної) варіаційної задані довільного, порядку, запропонований М. В. Остроградським, узагальнюється на випадок вироджених (сингулярних) лагранжіанів. Саме такі лагранжіани становлять найбільший інтерес для сучасної теорії елементарних частинок. Для спрощення формул розглядається гамільтонізація варіаційної задачі, заданої сингулярним лагранжіаном другого порядку. Рівняння руху в фазовому просторі виводяться шляхом узагальнення методу М. В. Остроградського. Знайдено повний;набір зв'язків у теорії. Institute of Mathematics, NAS of Ukraine 2001-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4323 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 8 (2001); 1034-1037 Український математичний журнал; Том 53 № 8 (2001); 1034-1037 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4323/5350 https://umj.imath.kiev.ua/index.php/umj/article/view/4323/5351 Copyright (c) 2001 Nesterenko V. V. |
| spellingShingle | Nesterenko, V. V. Нестеренко, В. В. Нестеренко, В. В. Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives |
| title | Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives |
| title_alt | Формализм Остроградского для сингулярных лагранжианов с высшими производными |
| title_full | Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives |
| title_fullStr | Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives |
| title_full_unstemmed | Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives |
| title_short | Ostrohrads'kyi Formalism for Singular Lagrangians with Higher Derivatives |
| title_sort | ostrohrads'kyi formalism for singular lagrangians with higher derivatives |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4323 |
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