Search

The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the versal deformation theory for matrices. Numerical examples are given. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The article focuses on the study conducted by Oene Bottema regarding the two-degree-of-freedom system related to the 4th order polynomial coefficients. It mentions that the study was associated with Ziegler's paradox n multiple degrees-of-freedom systems which needs the singularity theory done by V.I. Arnold in 1970. Result shows that it offers a final step to its quality understanding as a singularity, where it will remain for the simple specific cases without its understanding.

The article discusses the aspect of the study regarding the paradoxes in the dissipation-induced destabilization or who opened Whitney's umbrella conducted by Oene Bottema. It mentions that the study with damping was compared with the domain of marginal stability and asymptotic stability depending on its characteristic polynomials. It states that he resolved it through the singularity theory on the boundary of two-degrees-of freedom non-conservative systems including the Ziegler's pendulum.