The Geometry of Ordinary Variational Equations

1997
ISBN: 978-3-540-63832-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1678, 254 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 406 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Krupkova, Olga

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

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.