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Book Cover
Author Veselić, Krešimir

Title Damped oscillations of linear systems : a mathematical introduction / Krešimir Veselić
Published Berlin ; London ; New York : Springer, ©2011


Description 1 online resource (xv, 209 pages) : illustrations
Series Lecture notes in mathematics ; 2023
Lecture notes in mathematics (Springer-Verlag) ; 2023.
Contents The model -- Simultaneous diagonalisation (modal dumping) -- Phase space -- The singular mass case -- 'Indefinite Metric' -- Matrices and indefinite scalar products -- Oblique projections -- J-orthogonal projections -- Spectral properties and reduction of J-Hermitian matrices -- Definite spectra --General Hermitian matrix pairs -- Spectral decomposition of a general J-Hermitian Matrix -- The matrix exponential -- The quadratic eigenvalue problem -- Simple eigenvalue inclusions -- Spectral shift -- Resonances and resolvents -- Well-posedness -- 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 self-contained 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 203-206) 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
Form Electronic book
ISBN 9783642213359