Critical Point Theory for Lagrangian Systems

  • Marco Mazzucchelli

Part of the Progress in Mathematics book series (PM, volume 293)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Marco Mazzucchelli
    Pages 1-27
  3. Marco Mazzucchelli
    Pages 29-48
  4. Marco Mazzucchelli
    Pages 49-77
  5. Marco Mazzucchelli
    Pages 79-107
  6. Marco Mazzucchelli
    Pages 109-125
  7. Marco Mazzucchelli
    Pages 127-156
  8. Back Matter
    Pages 157-187

About this book

Introduction

Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange’s reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.

Keywords

Euler-Lagrange equations Lagrangian dynamics Morse theory periodic orbits

Authors and affiliations

  • Marco Mazzucchelli
    • 1
  1. 1.Eberly College of Science, Department of MathematicsPenn State UniversityUniversity ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0163-8
  • Copyright Information Springer Basel AG 2012
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0162-1
  • Online ISBN 978-3-0348-0163-8
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book