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Damped oscillations of linear system...

Veselic, Kresimir.

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Damped oscillations of linear systems : = a mathematical introduction /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Damped oscillations of linear systems :/ Kresimir Veselic.
Reminder of title:	a mathematical introduction /
Author:	Veselic, Kresimir.
Published:	Berlin ;Springer, : c2011.,
Description:	xv, 209 p. :ill. ;23 cm.
[NT 15003449]:	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.
Subject:	Harmonic oscillators - Textbooks. -
ISBN:	9783642213342 (pbk.) :

Damped oscillations of linear systems : = a mathematical introduction /
Veselic, Kresimir.

Damped oscillations of linear systems :a mathematical introduction /Kresimir Veselic. - Berlin ;Springer,c2011. - xv, 209 p. :ill. ;23 cm. - Lecture notes in mathematics ;2023. - Lecture notes in mathematics (Springer-Verlag) ;2002..

Includes bibliographical references (p. 203-206) and index.

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.

"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." --P. [4] of cover.

ISBN: 9783642213342 (pbk.) :EUR34.95

LCCN: 2011933133Subjects--Topical Terms:

1306011
Harmonic oscillators
--Textbooks.

LC Class. No.: QA865 / .V47 2011

Damped oscillations of linear systems : = a mathematical introduction /
LDR:02622cam a2200265 a 4500 001 980842
003 OCoLC
005 20111019043053.0
008 111115s2011 gw a b 001 0 eng d
010 $a 2011933133
020 $a 9783642213342 (pbk.) : $c EUR34.95
020 $a 3642213340 (pbk.)
029 1 $a AU@ $b 000047500718
035 $a (OCoLC)747814290 $z (OCoLC)731918818 $z (OCoLC)749912857
035 $a AS-BW-100-08
040 $a DLC $c CUD $d BTCTA $d YDXCP $d OHX $d OSU $d GZQ $d IXA $d BWX $d KUK $d MUU $d ZCU
049 $a FISA
050 # 4 $a QA865 $b .V47 2011
050 # 4 $a QA3 $b .L28 no.2023
100 1 $a Veselic, Kresimir. $3 1306255
245 1 0 $a Damped oscillations of linear systems : $b a mathematical introduction / $c Kresimir Veselic.
260 # $a Berlin ; $a London ; $a New York : $b Springer, $c c2011.
300 $a xv, 209 p. : $b ill. ; $c 23 cm.
490 1 $a Lecture notes in mathematics ; $v 2023
504 $a Includes bibliographical references (p. 203-206) and index.
505 0 # $a 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.
520 # $a "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." --P. [4] of cover.
650 # 0 $a Harmonic oscillators $v Textbooks. $3 1306011
650 # 0 $a Linear systems $v Textbooks. $3 1299146
830 0 $a Lecture notes in mathematics (Springer-Verlag) ; $v 2002. $3 1235985