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The Geometry of Ordinary Variational Equations

  • Book
  • © 1997

Overview

Authors:
  1. Olga Krupková
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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
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  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
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Keywords

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.

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