The Geometry of Ordinary Variational Equations

• Main Author: Krupkova, Olga (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Edition: 1st ed. 1997.
• Series: Lecture Notes in Mathematics, 1678
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Differential geometry.; Global analysis (Mathematics).; Manifolds (Mathematics).; Mechanics.; Mechanics, Applied.; Analysis.; Differential Geometry.; Global Analysis and Analysis on Manifolds.; Theoretical and Applied Mechanics.

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...

Table of Contents:

• 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.