LEADER 01169nam 2200337Ia 450 001 996391839503316 005 20221108090711.0 035 $a(CKB)1000000000669272 035 $a(EEBO)2264207924 035 $a(OCoLC)08038046 035 $a(EXLCZ)991000000000669272 100 $a19820104d1684 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 12$aA companion for prayer, or, Directions for improvement in grace and practical Godliness in time of extraordinary danger$b[electronic resource] /$fby Richard Allein 210 $aLondon $cPrinted by J.R. for T.C.$d1684 215 $a[2], 12 p 300 $aReproduction of originals in the Huntington Library. 330 $aeebo-0113 606 $aDevotional exercises 606 $aSpiritual life 615 0$aDevotional exercises. 615 0$aSpiritual life. 700 $aR. A$g(Richard Alleine),$f1611-1681.$01002641 801 0$bUMI 801 1$bUMI 801 2$bWaOLN 906 $aBOOK 912 $a996391839503316 996 $aA companion for prayer, or, Directions for improvement in grace and practical Godliness in time of extraordinary danger$92391929 997 $aUNISA LEADER 03571nam 2200577Ia 450 001 9910484254703321 005 20200520144314.0 010 $a9783642213359 010 $a3642213359 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 $a20110807d2011 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDamped oscillations of linear systems $ea mathematical introduction /$fKresimir Veselic 205 $a1st ed. 2011. 210 $aHeidelberg $cSpringer$d2011 215 $a1 online resource (XV, 200 p. 8 illus.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v2023 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642213342 311 08$a3642213340 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 (Springer-Verlag) ;$v2023. 606 $aDamping (Mechanics)$xMathematical models 606 $aAlgebras, Linear 615 0$aDamping (Mechanics)$xMathematical models. 615 0$aAlgebras, Linear. 676 $a519 700 $aVeselic$b Kresimir$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484254703321 996 $aDamped oscillations of linear systems$9261821 997 $aUNINA