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Lambda-Matrices and Vibrating Systems

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ISBN-10: 0486425460

ISBN-13: 9780486425467

Edition: 2002 (Unabridged)

Authors: Peter Lancaster

List price: $14.95
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Description:

Comprehensive treatment presents aspects and solutions of problems of linear vibrating systems with a finite number of degrees of freedom. Starts with development of necessary tools in matrix theory, followed by numerical procedures for relevant matrix formulations and relevant theory of differential equations. Minimum of mathematical abstraction; assumes a familiarity with matrix theory, elementary calculus. 1966 edition.
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Book details

List price: $14.95
Copyright year: 2002
Publisher: Dover Publications, Incorporated
Publication date: 12/20/2002
Binding: Hardcover
Pages: 208
Size: 4.75" wide x 8.25" long x 0.50" tall
Weight: 0.484

Preface to the Dover Edition
Preface
A Sketch of Some Matrix Theory
Definitions
Column and Row Vectors
Square Matrices
Linear Dependence, Rank, and Degeneracy
Special Kinds of Matrices
Matrices Dependent on a Scalar Parameter; Latent Roots and Vectors
Eigenvalues and Vectors
Equivalent Matrices and Similar Matrices
The Jordan Canonical Form
Bounds for Eigenvalues
Regular Pencils of Matrices and Eigenvalue Problems
Introduction
Orthogonality Properties of the Latent Vectors
The Inverse of a Simple Matrix Pencil
Application to the Eigenvalue Problem
The Constituent Matrices
Conditions for a Regular Pencil to be Simple
Geometric Implications of the Jordan Canonical Form
The Rayleigh Quotient
Simple Matrix Pencils with Latent Vectors in Common
Lambda-Matrices, I
Introduction
A Canonical Form for Regular [lambda]-Matrices
Elementary Divisors
Division of Square [lambda]-Matrices
The Cayley-Hamilton Theorem
Decomposition of [lambda]-Matrices
Matrix Polynomials with a Matrix Argument
Lambda-Matrices, II
Introduction
An Associated Matrix Pencil
The Inverse of a Simple [lambda]-Matrix in Spectral Form
Properties of the Latent Vectors
The Inverse of a Simple [lambda]-Matrix in Terms of its Adjoint
Lambda-matrices of the Second Degree
A Generalization of the Rayleigh Quotient
Derivatives of Multiple Eigenvalues
Some Numerical Methods for Lambda-matrices
Introduction
A Rayleigh Quotient Iterative Process
Numerical Example for the RQ Algorithm
The Newton-Raphson Method
Methods Using the Trace Theorem
Iteration of Rational Functions
Behavior at Infinity
A Comparison of Algorithms
Algorithms for a Stability Problem
Illustration of the Stability Algorithms
Appendix to Chapter 5
Ordinary Differential Equations with Constant Coefficients
Introduction
General Solutions
The Particular Integral when f(t) is Exponential
One-point Boundary Conditions
The Laplace Transform Method
Second Order Differential Equations
The Theory of Vibrating Systems
Introduction
Equations of Motion
Solutions under the Action of Conservative Restoring Forces Only
The Inhomogeneous Case
Solutions Including the Effects of Viscous Internal Forces
Overdamped Systems
Gyroscopic Systems
Sinusoidal Motion with Hysteretic Damping
Solutions for Some Non-conservative Systems
Some Properties of the Latent Vectors
On the Theory of Resonance Testing
Introduction
The Method of Stationary Phase
Properties of the Proper Numbers and Vectors
Determination of the Natural Frequencies
Determination of the Natural Modes
Appendix to Chapter 8
Further Results for Systems with Damping
Preliminaries
Global Bounds for the Latent Roots when B is Symmetric
The Use of Theorems on Bounds for Eigenvalues
Preliminary Remarks on Perturbation Theory
The Classical Perturbation Technique for Light Damping
The Case of Coincident Undamped Natural Frequencies
The Case of Neighboring Undamped Natural Frequencies
Bibliographical Notes
References
Index