Damped Oscillations of Linear Systems A Mathematical Introduction /

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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Veselić, Krešimir (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
Σειρά:Lecture Notes in Mathematics, 2023
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03541nam a22005055i 4500
001 978-3-642-21335-9
003 DE-He213
005 20151204181856.0
007 cr nn 008mamaa
008 110707s2011 gw | s |||| 0|eng d
020 |a 9783642213359  |9 978-3-642-21335-9 
024 7 |a 10.1007/978-3-642-21335-9  |2 doi 
040 |d GrThAP 
050 4 |a T57-57.97 
072 7 |a PBW  |2 bicssc 
072 7 |a MAT003000  |2 bisacsh 
082 0 4 |a 519  |2 23 
100 1 |a Veselić, Krešimir.  |e author. 
245 1 0 |a Damped Oscillations of Linear Systems  |h [electronic resource] :  |b A Mathematical Introduction /  |c by Krešimir Veselić. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg,  |c 2011. 
300 |a XV, 200 p. 8 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 2023 
505 0 |a 1 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 |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 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 |a Mathematics. 
650 0 |a Applied mathematics. 
650 0 |a Engineering mathematics. 
650 0 |a System theory. 
650 0 |a Mathematical physics. 
650 1 4 |a Mathematics. 
650 2 4 |a Applications of Mathematics. 
650 2 4 |a Systems Theory, Control. 
650 2 4 |a Mathematical Applications in the Physical Sciences. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783642213342 
830 0 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 2023 
856 4 0 |u http://dx.doi.org/10.1007/978-3-642-21335-9  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
912 |a ZDB-2-LNM 
950 |a Mathematics and Statistics (Springer-11649)