## Browse content

### Table of contents

#### Actions for selected chapters

- Full text access
- Book chapterAbstract only
#### CHAPTER 1 - A SKETCH OF SOME MATRIX THEORY

Pages 1-22 - Book chapterAbstract only
#### CHAPTER 2 - REGULAR PENCILS OF MATRICES AND EIGENVALUE PROBLEMS

Pages 23-41 - Book chapterAbstract only
#### CHAPTER 3 - LAMBDA-MATRICES, I

Pages 42-55 - Book chapterAbstract only
#### CHAPTER 4 - LAMBDA-MATRICES, II

Pages 56-74 - Book chapterAbstract only
#### CHAPTER 5 - SOME NUMERICAL METHODS FOR LAMBDA-MATRICES

Pages 75-99 - Book chapterAbstract only
#### CHAPTER 6 - ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

Pages 100-115 - Book chapterAbstract only
#### CHAPTER 7 - THE THEORY OF VIBRATING SYSTEMS

Pages 116-142 - Book chapterAbstract only
#### CHAPTER 8 - ON THE THEORY OF RESONANCE TESTING

Pages 143-157 - Book chapterAbstract only
#### CHAPTER 9 - FURTHER RESULTS FOR SYSTEMS WITH DAMPING

Pages 158-183 - Book chapterNo access
#### BIBLIOGRAPHICAL NOTES

Pages 184-186 - Book chapterNo access
#### REFERENCES

Pages 187-190 - Book chapterNo access
#### INDEX

Pages 191-193 - Book chapterNo access
#### OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS

Pages 194-196

## About the book

### Description

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.

## Details

### ISBN

978-0-08-011664-8

### Language

English

### Published

1966

### Copyright

Copyright © 1966 Elsevier Inc. All rights reserved.

### Imprint

Pergamon