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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ISBN-13
978-3-540-69657-5 (9783540696575)
DOI
Schweitzer Klassifikation
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.
