Author	Krupkovรก, Olga. author
Title	The Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupkovรก
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1997
Connect to	http://dx.doi.org/10.1007/BFb0093438
Descript	CCLXIV, 254 p. online resource

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

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 ?: RรMยปR

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Global analysis (Mathematics)
5. Manifolds (Mathematics)
6. Differential geometry
7. Mechanics
8. Mechanics
9. Applied
10. Mathematics
11. Analysis
12. Differential Geometry
13. Global Analysis and Analysis on Manifolds
14. Theoretical and Applied Mechanics