000 | 03712nam a22004815i 4500 | ||
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001 | 978-3-642-21335-9 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 110707s2011 gw | s |||| 0|eng d | ||
020 |
_a9783642213359 _9978-3-642-21335-9 |
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024 | 7 |
_a10.1007/978-3-642-21335-9 _2doi |
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050 | 4 | _aT57-57.97 | |
072 | 7 |
_aPBW _2bicssc |
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_aMAT003000 _2bisacsh |
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_aPBW _2thema |
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082 | 0 | 4 |
_a519 _223 |
100 | 1 |
_aVeselić, Krešimir. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aXV, 200 p. 8 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2023 |
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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 |