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:

• Krupkova, Olga.
• SpringerLink (Online service)

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)