| 书目名称 | Periodic Solutions of the N-Body Problem |
| 编辑 | Kenneth R. Meyer |
| 视频video | |
| 概述 | Includes supplementary material: |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the |
| 出版日期 | Book 1999 |
| 关键词 | Celestial Mechanics; Hamiltonian Systems; N-Body Problem; Symmetries; mechanics |
| 版次 | 1 |
| doi | https://doi.org/10.1007/BFb0094677 |
| isbn_softcover | 978-3-540-66630-1 |
| isbn_ebook | 978-3-540-48073-0Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer-Verlag Berlin Heidelberg 1999 |
发表于 2025-3-21 16:03:41
