TY  - BOOK
AU  - Krupková,Olga
ED  - SpringerLink (Online service)
TI  - The Geometry of Ordinary Variational Equations
T2  - Lecture Notes in Mathematics,
SN  - 9783540696575
AV  - QA641-670 
U1  - 516.36 23
PY  - 1997///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis
KW  - Global differential geometry
KW  - Mechanics, applied
KW  - Differential Geometry
KW  - Global Analysis and Analysis on Manifolds
KW  - Theoretical and Applied Mechanics
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0093438
ER  -