The Geometry of Ordinary Variational Equations / Edition 1

by Olga Krupkova

Overview

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.

Product Details

ISBN-13:	9783540638322
Publisher:	Springer Berlin Heidelberg
Publication date:	12/09/1997
Series:	Lecture Notes in Mathematics , #1678
Edition description:	1997
Pages:	254
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

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—: R×M»R.