The Geometry of Ordinary Variational Equations. 1st ed. 1997
- 種類:
- 電子ブック
- 責任表示:
- by Olga Krupkova
- 出版情報:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997
- 著者名:
- シリーズ名:
- Lecture Notes in Mathematics ; 1678
- ISBN:
- 9783540696575 [3540696571]
- 注記:
- Basic geometric tools -- Lagrangean dynamics on fibered manifolds -- Variational Equations -- Hamiltonian systems -- Regular Lagrangean systems -- Singular Lagrangean systems -- Symmetries of Lagrangean systems -- Geometric intergration methods -- Lagrangean systems on ?: R×M»R.
The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations. - ローカル注記:
- 学内専用E-BOOKS (local access only)
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