Lambda-matrices and vibrating systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Pergamon Press
1966
|
| Series: | International series of monographs on pure and applied mathematics
94 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 187 - 190 |
| Physical Description: | XIII, 196 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Lambda-matrices and vibrating systems |c Peter Lancaster |
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Record in the Search Index
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| adam_text | CONTENTS
Preface xi
Chapter 1. A Sketch of Some Matrix Theoby 1
1.1 Definitions 1
1.2 Column and Row Vectors 3
1.3 Square Matrices 4
1.4 Linear Dependence, Rank, and Degeneracy 7
1.5 Special Kinds of Matrices 8
1.6 Matrices Dependent on a Scalar Parameter; Latent Roots and
Vectors 10
1.7 Eigenvalues and Vectors 11
1.8 Equivalent Matrices and Similar Matrices 14
1.9 The Jordan Canonical Form 18
1.10 Bounds for Eigenvalues 20
Chapter 2. Regular Pencils of Matrices
and Eigenvalue Problems 23
2.1 Introduction 23
2.2 Orthogonality Properties of the Latent Vectors 24
2.3 The Inverse of a Simple Matrix Pencil 27
2.4 Application to the Eigenvalue Problem 28
2.5 The Constituent Matrices 33
2.6 Conditions for a Regular Pencil to be Simple 35
2.7 Geometric Implications of the Jordan Canonical Form 38
2.8 The Rayleigh Quotient 39
2.9 Simple Matrix Pencils with Latent Vectors in Common 40
Chapter 3. Lambda matrices, I 42
3.1 Introduction 42
3.2 A Canonical Form for Regular A Matrices 43
3.3 Elementary Divisors 45
3.4 Division of Square A Matrices 47
3.5 The Cayley Hamilton Theorem 49
3.6 Decomposition of A Matrices 50
3.7 Matrix Polynomials with a Matrix Argument 53
Chapter 4. Lambda matrices, II 56
4.1 Introduction 56
4.2 An Associated Matrix Pencil 56
4.3 The Inverse of a Simple A Matrix in Spectral Form 59
vii
viii contents
4.4 Properties of the Latent Vectors 64
4.5 The Inverse of a Simple A Matrix in Terms of its Adjoint 67
4.6 Lamhda matrices of the Second Degree 68
4.7 A Generalization of the Rayleigh Quotient 71
4.8 Derivatives of Multiple Eigenvalues 73
Chapter 5. Some Numerical Methods for Lambda matrices 75
5.1 Introduction 75
5.2 A Rayleigh Quotient Iterative Process 77
5.3 Numerical Example for the RQ Algorithm 79
5.4 The Newton Raphson Method 81
5.5 Methods Using the Trace Theorem 82
5.6 Iteration of Rational Functions 86
5.7 Behavior at Infinity 89
5.8 A Comparison of Algorithms 90
5.9 Algorithms for a Stability Problem 92
5.10 Illustration of the Stability Algorithms 95
Appendix to Chapter 5 98
Chapter 6. Ordinary Differential Equations with Constant
Coefficients 100
6.1 Introduction 100
6.2 General Solutions 101
6.3 The Particular Integral when f(t) is Exponential 108
6.4 One point Boundary Conditions 109
6.5 The Laplace Transform Method 111
6.6 Second Order Differential Equations 114
Chapter 7. The Theory of Vibrating Systems 116
7.1 Introduction 116
7.2 Equations of Motion 117
7.3 Solutions under the Action of Conservative Restoring Forces
Only 122
7.4 The Inhomogeneous Case 124
7.5 Solutions Including the Effects of Viscous Internal Forces 125
7.6 Overdamped Systems 130
7.7 Gyroscopic Systems 135
7.8 Sinusoidal Motion with Hysteretic Damping 137
7.9 Solutions for Some Non conservative Systems 138
7.10 Some Properties of the Latent Vectors 140
Chapter 8. On the Theory of Resonance Testing 143
8.1 Introduction 143
8.2 The Method of Stationary Phase 144
8.3 Properties of the Proper Numbers and Vectors 148
8.4 Determination of the Natural Frequencies 152
8.5 Determination of the Natural Modes 153
Appendix to Chapter 8 156
CONTENTS . ix
Chapter 9. Further Results for Systems with Damping 158
9.1 Preliminaries 158
9.2 Global Bounds for the Latent Roots when B is Symmetric 160
9.3 The Use of Theorems on Bounds for Eigenvalues 162
9.4 Preliminary Remarks on Perturbation Theory 168
9.5 The Classical Perturbation Technique for Light Damping 171
9.6 The Case of Coincident Undamped Natural Frequencies 174
9.7 The Case of Neighboring Undamped Natural Frequencies 178
Bibliographical Notes 184
References 187
Index 191
Other Titles Published in this Series 194
|
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| id | DE-604.BV015262805 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:09:06Z |
| institution | BVB |
| language | English |
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| physical | XIII, 196 S. |
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| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series of monographs on pure and applied mathematics |
| series2 | International series of monographs on pure and applied mathematics |
| spelling | Lancaster, Peter 1929- Verfasser (DE-588)123638348 aut Lambda-matrices and vibrating systems Peter Lancaster Oxford [u.a.] Pergamon Press 1966 XIII, 196 S. txt rdacontent n rdamedia nc rdacarrier International series of monographs on pure and applied mathematics 94 Literaturverz. S. 187 - 190 Matrices Vibration Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Schwingung (DE-588)4053999-4 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s Schwingung (DE-588)4053999-4 s DE-604 International series of monographs on pure and applied mathematics 94 (DE-604)BV001888024 94 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010097610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lancaster, Peter 1929- Lambda-matrices and vibrating systems International series of monographs on pure and applied mathematics Matrices Vibration Matrix Mathematik (DE-588)4037968-1 gnd Schwingung (DE-588)4053999-4 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4053999-4 |
| title | Lambda-matrices and vibrating systems |
| title_auth | Lambda-matrices and vibrating systems |
| title_exact_search | Lambda-matrices and vibrating systems |
| title_full | Lambda-matrices and vibrating systems Peter Lancaster |
| title_fullStr | Lambda-matrices and vibrating systems Peter Lancaster |
| title_full_unstemmed | Lambda-matrices and vibrating systems Peter Lancaster |
| title_short | Lambda-matrices and vibrating systems |
| title_sort | lambda matrices and vibrating systems |
| topic | Matrices Vibration Matrix Mathematik (DE-588)4037968-1 gnd Schwingung (DE-588)4053999-4 gnd |
| topic_facet | Matrices Vibration Matrix Mathematik Schwingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010097610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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