Lecture Notes in Mathematics

By: Olga Krupkova

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Paperback | 27 November 1997

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264 Pages

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24.13 x 15.88 x 1.27

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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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Introduction	p. 1
Basic Geometric Tools	p. 20
Lagrangean Dynamics on Fibered Manifolds	p. 41
Variational Equations	p. 52
Hamiltonian Systems	p. 80
Regular Lagrangean Systems	p. 97
Singular Lagrangean Systems	p. 129
Symmetries of Lagrangean Systems	p. 149
Geometric Integration Methods	p. 174
Lagrangean Systems on [actual symbol not reproducible]	p. 208
Bibliography	p. 229
Index	p. 246
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

At a Glance

Paperback

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