Journal ArticleDOI
Linear dynamical systems and an approximation problem for linear transformations
TLDR
In this paper, the authors discuss an approximating procedure which is often used in the analysis of damped linear dynamical systems arising in engineering, and discuss an approximation procedure that is used in their work.Abstract:
This paper discusses an approximating procedure which is often used in the analysis of damped linear dynamical systems arising in engineering.read more
Citations
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Journal ArticleDOI
Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)
TL;DR: This book discusses Maximization, Minimization, and Motivation, which is concerned with the optimization of Symmetric Matrices, and its applications in Programming and Mathematical Economics.
Journal ArticleDOI
On the approximation of damped linear dynamical systems
TL;DR: In this paper, two approximating schemes for damped linear dynamical systems are described, one due to Rayleigh, which approximates the damping and the stiffness, and the other due to the stiffness.
Journal ArticleDOI
On damped linear dynamical systems
TL;DR: In this article, an upper bound on the frequency response of damped linear dynamical systems which do not violate the convenience hypothesis too severely is derived for the error committed when such a system is described approximately by a differential equation.
Journal ArticleDOI
On a minimization problem associated with linear dynamical systems
TL;DR: This paper considers the problem of approximating a given pair of symmetry tensors by a pair of symmetric Cartesian tensors that commute.
Journal ArticleDOI
Remarks on approximations for linear dynamical systems
TL;DR: In this article, two techniques for approximate analysis of damped linear dynamical systems are compared, and two approaches for approximating the exact analysis of linear systems with damped dynamical components are presented.
References
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Book
Introduction to Matrix Analysis
TL;DR: In this article, the Second Edition Preface is presented, where Maximization, Minimization, and Motivation are discussed, as well as a method of Hermite and Quadratic Form Index.
Book
Theory of sound
TL;DR: In this article, the Laplace's functions of T, F, V are simultaneously reducible to sums of squares, where T is the length of a string, F is the degree of freedom of the string, and V is the size of the chord.
Journal ArticleDOI
Classical Normal Modes in Damped Linear Dynamic Systems
TL;DR: In this article, the necessary and sufficient conditions under which both discrete and continuous damped linear dynamic systems possess classical normal modes were determined for both continuous and discrete linear systems, respectively.
Journal ArticleDOI
Modal damping for torsionally coupled buildings on elastic foundation
TL;DR: In this article, a method to determine the approximate normal modes and the modal damping for torsionally coupled buildings on an elastic foundation is presented, where the response quantity to be matched is selected in a consistent and logical manner.
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