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  • Book
  • © 1997

The Geometry of Ordinary Variational Equations

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction

    • Olga Krupková
    Pages 1-19
  3. Basic geometric tools

    • Olga Krupková
    Pages 20-40
  4. Lagrangean dynamics on fibered manifolds

    • Olga Krupková
    Pages 41-51
  5. Variational Equations

    • Olga Krupková
    Pages 52-79
  6. Hamiltonian systems

    • Olga Krupková
    Pages 80-96
  7. Regular Lagrangean systems

    • Olga Krupková
    Pages 97-128
  8. Singular Lagrangean systems

    • Olga Krupková
    Pages 129-148
  9. Symmetries of Lagrangean systems

    • Olga Krupková
    Pages 149-173
  10. Geometric intergration methods

    • Olga Krupková
    Pages 174-207
  11. Lagrangean systems on π: R×M»R

    • Olga Krupková
    Pages 208-228
  12. Back Matter

    Pages 229-251

About this book

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

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions