Linear Vibrations

By: G M Sklyar, Werner Krabs

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Hardcover | 1 December 2001

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Science Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics Differential Calculus & Equations

Preface	p. vii
Null-Controllability of Undamped Linear Vibrations	p. 1
Distributed Control	p. 1
Boundary H[superscript 2]-Control	p. 6
The Problem of Null-Controllability	p. 9
On the Solution of the Problem of Null-Controllability	p. 11
Boundary Null-Controllability with H[superscript 1]-Controls	p. 21
Approximate Boundary Null-Controllability with H[superscript 2]-Controls	p. 27
Examples	p. 32
Null-Controllability of Damped Linear Vibrations	p. 39
Distributed Control	p. 39
The Model Equation and its Solution	p. 39
The Problem of Null-Controllability	p. 45
Boundary Control	p. 49
The Model Equations	p. 49
On the Solution of the Model Equations	p. 51
The Problem of Null-Controllability	p. 53
Approximate Null-Controllability	p. 56
Examples	p. 61
On the Controllability of a Rotating Beam	p. 69
The Model Equations and their Solution	p. 69
The Problem of Controllability from Rest to Rest	p. 74
The Asymptotic Behaviour of the Eigenvalues of the Operator A in (3.3)	p. 76
On Controllability from Rest to Rest	p. 84
On Approximate Controllability from Rest to an Arbitrary Position	p. 85
The Limit Case [gamma superscript 2] = EA/K = [infinity]	p. 93
On Stabilizability	p. 94
On Control and Stabilization with the Aid of the Torque	p. 106
Appendix	p. 125
Linear Operators	p. 125
Semigroups of Linear Operators	p. 130
Basic Definitions	p. 130
On the Generation of C[superscript 0]-Semigroups	p. 131
Application to the Solution of Evolution Equations	p. 133
Strong Stabilizability of Evolution Equations	p. 135
Modeling a Rotating Beam	p. 147
Bibliographical Remarks and Further Problems	p. 152
Bibliography	p. 159
Index	p. 161
Table of Contents provided by Syndetics. All Rights Reserved.

Linear Vibrations

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