Description 
1 online resource (xv, 209 pages) : illustrations 
Series 
Lecture notes in mathematics ; 2023 

Lecture notes in mathematics (SpringerVerlag) ; 2023.

Contents 
The model  Simultaneous diagonalisation (modal dumping)  Phase space  The singular mass case  'Indefinite Metric'  Matrices and indefinite scalar products  Oblique projections  Jorthogonal projections  Spectral properties and reduction of JHermitian matrices  Definite spectra General Hermitian matrix pairs  Spectral decomposition of a general JHermitian Matrix  The matrix exponential  The quadratic eigenvalue problem  Simple eigenvalue inclusions  Spectral shift  Resonances and resolvents  Wellposedness  Modal approximation  Modal approximation  Modal approximation and overdampedness  Passive control  Perturbing matrix exponential Notes and remarks 
Summary 
"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 systems model, a largely selfcontained mathematical theory for this model is presented. this includes the geometry of the underlying indefinite 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."Page 4 of cover 
Bibliography 
Includes bibliographical references (pages 203206) and index 
Notes 
English 

Print version record 
Subject 
Harmonic oscillators  Textbooks


Linear systems  Textbooks


Sistemas lineales  Libros de texto


Harmonic oscillators


Linear systems

Genre/Form 
Textbooks


Textbooks.

Form 
Electronic book

ISBN 
9783642213359 

3642213359 
