The Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupková.
Material type: TextSeries: Lecture Notes in Mathematics ; 1678Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997Description: CCLXIV, 254 p. online resourceContent type:- text
- computer
- online resource
- 9783540696575
- 515 23
- QA299.6-433
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.
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.
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