The Geometry of Ordinary Variational Equations

• Κύριος συγγραφέας: Krupkova, Olga (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Έκδοση: 1st ed. 1997.
• Σειρά: Lecture Notes in Mathematics, 1678
• Θέματα: 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 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 ?: R×M»R.