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020 _a9783642213359
_9978-3-642-21335-9
024 7 _a10.1007/978-3-642-21335-9
_2doi
050 4 _aT57-57.97
072 7 _aPBW
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPBW
_2thema
082 0 4 _a519
_223
100 1 _aVeselić, Krešimir.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDamped Oscillations of Linear Systems
_h[electronic resource] :
_bA Mathematical Introduction /
_cby Krešimir Veselić.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXV, 200 p. 8 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2023
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aSystems theory.
650 1 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
650 2 4 _aSystems Theory, Control.
_0http://scigraph.springernature.com/things/product-market-codes/M13070
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642213342
776 0 8 _iPrinted edition:
_z9783642213366
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2023
856 4 0 _uhttps://doi.org/10.1007/978-3-642-21335-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12023
_d12023