LEADER 04216nam  22006375  450 
001 996466505703316
005 20200706204825.0
010   $a3-642-21335-9
024 7 $a10.1007/978-3-642-21335-9
035   $a(CKB)2550000000040752
035   $a(SSID)ssj0000506041
035   $a(PQKBManifestationID)11313187
035   $a(PQKBTitleCode)TC0000506041
035   $a(PQKBWorkID)10514689
035   $a(PQKB)10191778
035   $a(DE-He213)978-3-642-21335-9
035   $a(MiAaPQ)EBC3066959
035   $a(PPN)15631813X
035   $a(EXLCZ)992550000000040752
100   $a20110707d2011      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aDamped Oscillations of Linear Systems$b[electronic resource] $eA Mathematical Introduction /$fby Kre?imir Veseli?
205   $a1st ed. 2011.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011.
215   $a1 online resource (XV, 200 p. 8 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2023
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-21334-0 
320   $aIncludes bibliographical references and index.
327   $a1 The model -- 2 Simultaneous diagonalisation (Modal damping) -- 3 Phase space -- 4 The singular mass case -- 5 "Indefinite metric" -- 6 Matrices and indefinite scalar products -- 7 Oblique projections -- 8 J-orthogonal projections -- 9 Spectral properties and reduction of J-Hermitian matrices -- 10 Definite spectra -- 11 General Hermitian matrix pairs -- 12 Spectral decomposition of a general J-Hermitian matrix -- 13 The matrix exponential -- 14 The quadratic eigenvalue problem -- 15 Simple eigenvalue inclusions -- 16 Spectral shift -- 17 Resonances and resolvents -- 18 Well-posedness  -- 19 Modal approximation -- 20 Modal approximation and overdampedness -- 21 Passive control -- 22 Perturbing matrix exponential -- 23 Notes and remarks.
330   $aThe theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2023
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aSystem theory
606   $aMathematical physics
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
606   $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070
606   $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615  0$aSystem theory.
615  0$aMathematical physics.
615 14$aApplications of Mathematics.
615 24$aSystems Theory, Control.
615 24$aMathematical Applications in the Physical Sciences.
676   $a519
700   $aVeseli?$b Kre?imir$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478957
906   $aBOOK
912   $a996466505703316
996   $aDamped oscillations of linear systems$9261821
997   $aUNISA