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.
• Physical Description: CCLXIV, 254 p. online resource.
• ISBN: 9783540696575
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0093438

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.