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  • Book
  • © 1991

Hamiltonian and Lagrangian Flows on Center Manifolds

with Applications to Elliptic Variational Problems

Authors:

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1489)

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  • ISBN: 978-3-540-46441-9
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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction

    • Alexander Mielke
    Pages 1-6
  3. Notations and basic facts on center manifolds

    • Alexander Mielke
    Pages 9-16
  4. The linear theory

    • Alexander Mielke
    Pages 17-26
  5. Hamiltonian flows on center manifolds

    • Alexander Mielke
    Pages 27-40
  6. Hamiltonian systems with symmetries

    • Alexander Mielke
    Pages 41-59
  7. Lagrangian systems

    • Alexander Mielke
    Pages 61-83
  8. Nonautonomous systems

    • Alexander Mielke
    Pages 85-92
  9. Capillarity surface waves

    • Alexander Mielke
    Pages 103-108
  10. Necking of strips

    • Alexander Mielke
    Pages 109-119
  11. Saint-Venant's problem

    • Alexander Mielke
    Pages 121-131
  12. Back Matter

    Pages 133-142

About this book

The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.

Keywords

  • Bifurcation
  • Center Manifold
  • Hamiltonian and Langrangian Systems
  • Lie group
  • Nonlinear Elasticity
  • Variational Problems
  • classical mechanics
  • manifold

Bibliographic Information

  • Book Title: Hamiltonian and Lagrangian Flows on Center Manifolds

  • Book Subtitle: with Applications to Elliptic Variational Problems

  • Authors: Alexander Mielke

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0097544

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54710-5

  • eBook ISBN: 978-3-540-46441-9

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 140

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

Buying options

eBook USD 29.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-46441-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 39.99
Price excludes VAT (USA)