Cover for Lambda-Matrices and Vibrating Systems

Lambda-Matrices and Vibrating Systems

Volume 94 in International Series of Monographs on Pure and Applied Mathematics

Book1966

Author:

PETER LANCASTER

Lambda-Matrices and Vibrating Systems

Volume 94 in International Series of Monographs on Pure and Applied Mathematics

Book1966

 

Cover for Lambda-Matrices and Vibrating Systems

Author:

PETER LANCASTER

About the book

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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 ... read full description

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  1. Full text access
  2. Book chapterAbstract only

    CHAPTER 1 - A SKETCH OF SOME MATRIX THEORY

    Pages 1-22

  3. Book chapterAbstract only

    CHAPTER 2 - REGULAR PENCILS OF MATRICES AND EIGENVALUE PROBLEMS

    Pages 23-41

  4. Book chapterAbstract only

    CHAPTER 3 - LAMBDA-MATRICES, I

    Pages 42-55

  5. Book chapterAbstract only

    CHAPTER 4 - LAMBDA-MATRICES, II

    Pages 56-74

  6. Book chapterAbstract only

    CHAPTER 5 - SOME NUMERICAL METHODS FOR LAMBDA-MATRICES

    Pages 75-99

  7. Book chapterAbstract only

    CHAPTER 6 - ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

    Pages 100-115

  8. Book chapterAbstract only

    CHAPTER 7 - THE THEORY OF VIBRATING SYSTEMS

    Pages 116-142

  9. Book chapterAbstract only

    CHAPTER 8 - ON THE THEORY OF RESONANCE TESTING

    Pages 143-157

  10. Book chapterAbstract only

    CHAPTER 9 - FURTHER RESULTS FOR SYSTEMS WITH DAMPING

    Pages 158-183

  11. Book chapterNo access

    BIBLIOGRAPHICAL NOTES

    Pages 184-186

  12. Book chapterNo access

    REFERENCES

    Pages 187-190

  13. Book chapterNo access

    INDEX

    Pages 191-193

  14. 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

Authors

PETER LANCASTER

Associate Professor of Mathematics, University of Alberta, Calgary