Accession Number:

AD0787037

Title:

Quadratic Eigenproblems,

Descriptive Note:

Corporate Author:

STANFORD UNIV CALIF DEPT OF APPLIED MECHANICS

Personal Author(s):

Report Date:

1974-08-01

Pagination or Media Count:

50.0

Abstract:

This paper contains a theory for the study, in analytical terms, of the eigensystem of a multiparameter quadratic eigenproblem. Previous work in this general area has focused mainly on first order eigenproblems. In the present work, eigenvalues and eigenvectors are expressed in the form of infinite series in which parameters entering the elements of various matrices play the roles of independent variables, and it is shown how the coefficients may be evaluated. The methods of derivation are given in sufficient detail to allow extension to either higher derivatives or higher order eigenproblems. Among the results presented are formulae for the second derivatives of eigenvectors, which have not been presented previously. Formulae applicable to special cases of first order eigenproblems are given also. To illustrate the use of the theory, the behavior of a two degree of freedom gyroscopic system is considered in detail. Specifically, the effect of velocity dependent forces upon the stability of certain motions is studied. Author

Subject Categories:

  • Theoretical Mathematics
  • Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE