Skip to main content
  • Book
  • © 2011

Damped Oscillations of Linear Systems

A Mathematical Introduction

  • No recent texts on this topic

  • Multidisciplinarity

  • Self-containedness

  • Includes supplementary material: sn.pub/extras

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

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
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

This is a preview of subscription content, access via your institution.

Table of contents (23 chapters)

  1. Front Matter

    Pages i-xv
  2. The Model

    • Krešimir Veselić
    Pages 1-13
  3. Simultaneous Diagonalisation (Modal Damping)

    • Krešimir Veselić
    Pages 15-22
  4. Phase Space

    • Krešimir Veselić
    Pages 23-28
  5. The Singular Mass Case

    • Krešimir Veselić
    Pages 29-37
  6. ‘Indefinite Metric’

    • Krešimir Veselić
    Pages 39-48
  7. Matrices and Indefinite Scalar Products

    • Krešimir Veselić
    Pages 49-54
  8. Oblique Projections

    • Krešimir Veselić
    Pages 55-60
  9. J-Orthogonal Projections

    • Krešimir Veselić
    Pages 61-65
  10. Definite Spectra

    • Krešimir Veselić
    Pages 73-88
  11. General Hermitian Matrix Pairs

    • Krešimir Veselić
    Pages 89-92
  12. The Matrix Exponential

    • Krešimir Veselić
    Pages 113-120
  13. The Quadratic Eigenvalue Problem

    • Krešimir Veselić
    Pages 121-127
  14. Simple Eigenvalue Inclusions

    • Krešimir Veselić
    Pages 129-134
  15. Spectral Shift

    • Krešimir Veselić
    Pages 135-138
  16. Resonances and Resolvents

    • Krešimir Veselić
    Pages 139-141
  17. Well-Posedness

    • Krešimir Veselić
    Pages 143-143
  18. Modal Approximation

    • Krešimir Veselić
    Pages 145-157

About this book

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

Reviews

From the reviews:

“The present book is a very detailed study of this damped system in 22cChapters and an addendum devoted to notes and remarks. The theoretical aspects are very interestingly combined with practical examples for several domains. … An important aspect is that each chapter contains a large number of exercises, some of them obligatory since they are used later. So, this material can be very useful for a course to students from different special areas.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1232, 2012)

“This book is devoted to a mathematical study of damped oscillations described by linear systems of ordinary differential equations. The topic is of vital interest in optimization, control theory and, of course, in the stability of mechanical structures. … Examples and exercises are integral parts of the text and some of them introduce the reader to research questions.” (Piotr Biler, Mathematical Reviews, Issue 2012 h)

Authors and Affiliations

  • Fakultät für Mathematik und Informatik, Fernuniversität Hagen, Hagen, Germany

    Krešimir Veselić

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
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