Damped Oscillations of Linear Systems

A Mathematical Introduction

  • Krešimir Veselić

Part of the Lecture Notes in Mathematics book series (LNM, volume 2023)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Krešimir Veselić
    Pages 1-13
  3. Krešimir Veselić
    Pages 15-22
  4. Krešimir Veselić
    Pages 23-28
  5. Krešimir Veselić
    Pages 29-37
  6. Krešimir Veselić
    Pages 39-48
  7. Krešimir Veselić
    Pages 49-54
  8. Krešimir Veselić
    Pages 55-60
  9. Krešimir Veselić
    Pages 61-65
  10. Krešimir Veselić
    Pages 73-88
  11. Krešimir Veselić
    Pages 89-92
  12. Krešimir Veselić
    Pages 113-120
  13. Krešimir Veselić
    Pages 121-127
  14. Krešimir Veselić
    Pages 129-134
  15. Krešimir Veselić
    Pages 135-138
  16. Krešimir Veselić
    Pages 139-141
  17. Krešimir Veselić
    Pages 143-143
  18. Krešimir Veselić
    Pages 145-157

About this book

Introduction

The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics.
This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.

Keywords

15-XX, 47-XX, 70-XX Damped Systems Linear Systems

Authors and affiliations

  • Krešimir Veselić
    • 1
  1. 1.Fakultät für Mathematik und InformatikFernuniversität HagenHagenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-21335-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21334-2
  • Online ISBN 978-3-642-21335-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book