The Geometry of Ordinary Variational Equations

  • Authors
  • Olga Krupková

Part of the Lecture Notes in Mathematics book series (LNM, volume 1678)

Table of contents

  1. Front Matter
    Pages I-X
  2. Olga Krupková
    Pages 1-19
  3. Olga Krupková
    Pages 20-40
  4. Olga Krupková
    Pages 41-51
  5. Olga Krupková
    Pages 52-79
  6. Olga Krupková
    Pages 80-96
  7. Olga Krupková
    Pages 97-128
  8. Olga Krupková
    Pages 129-148
  9. Olga Krupková
    Pages 149-173
  10. Olga Krupková
    Pages 174-207
  11. Olga Krupková
    Pages 208-228
  12. Back Matter
    Pages 229-251

About this book

Introduction

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.

Keywords

Hamilton-Jacobi theory Hamiltonian mechanics Lagrangian mechanics calculus differential equation differential geometry higher-order variational equations manifold regularity

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093438
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63832-2
  • Online ISBN 978-3-540-69657-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book