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Differential-geometric structure associated with Lagrangian, and its dynamic interpretationстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 14 августа 2017 г.
- Автор: Rybnikov A.K.
- Журнал: Russian Mathematics
- Том: 61
- Номер: 3
- Год издания: 2017
- Первая страница: 20
- Последняя страница: 30
- DOI: 10.3103/S1066369X17030033
- Аннотация: The paper is devoted to investigation of differential-geometric structure associated with Lagrangian t depending on n functions of one variable L and their derivatives by means of Cartan–Laptev method. We construct a fundamental object of a structure associated with Lagrangian. We also construct a covector Ei (i = 1,..., n) embraced by prolonged fundamental object so that the system of equalities Ei = 0 is an invariant representation of the Euler equations for the variational functional. Due to this, there is no necessity to connect Euler equations with the variational problem. Moreover,we distinguish in an invariant way the class of special Lagrangians generating connection in the bundle of centroaffine structure over the base M. In the case when Lagrangian L is special, there exists a relative invariant Π defined on M which generates a covector field on M and fibered metric in the bundle of centroaffine structure over the base M.
- Добавил в систему: Родионов Тимофей Викторович