The geometry of ordinary variational equations
Author(s)
Bibliographic Information
The geometry of ordinary variational equations
（Lecture notes in mathematics, 1678）
Springer-Verlag, c1997
Available at / 89 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1678RM971226
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Note
Includes bibliographical references (p. [229]-245) and index
Description and Table of Contents
Description
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.
Table of Contents
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 ?: RxM"R.
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