| 书目名称 | Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature | | 编辑 | Tatiana G. Vozmischeva | | 视频video | | | 丛书名称 | Astrophysics and Space Science Library | | 图书封面 |  | | 描述 | Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don‘t depend expli | | 出版日期 | Book 2003 | | 关键词 | Area; Celestial mechanics; differential geometry; dynamics; geometry; mechanics; topology | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-017-0303-1 | | isbn_softcover | 978-90-481-6382-3 | | isbn_ebook | 978-94-017-0303-1Series ISSN 0067-0057 Series E-ISSN 2214-7985 | | issn_series | 0067-0057 | | copyright | Springer Science+Business Media Dordrecht 2003 |
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发表于 2025-3-21 17:12:46
