Determining dynamic characteristics of mechanical systems by the method of constructing one-dimensional spectral portraits of matrices

Abstract

A number of important properties of vibrations of linear systems (the quality of stability of the systems, their conditionality with respect to the eigenvalues of the matrices, and the possibility of modeling systems with a large number of degrees of freedom by their subsystems with a smaller number of degrees of freedom), which can be determined by a new mathematical tool called "One-dimensional spectral portraits of matrices" developed under the guidance of S. K. Godunov, are considered. An example is given on constructing one-dimensional spectral portraits for matrices that describe aeroelastic vibrations of hydrodynamic cascades.

Algorithm 918

“…The first two cases are popular and important in the study of discrete-time and continuous-time stability, see Dai [1989], Godunov [1997], Ionescu et al [1999], Kailath [1980] and Kurzin [2008]. The two latter cases are important in some particular situations, for example, the case when γ is a finite interval may be reduced to the spectral dichotomy by an ellipse, see Godunov and Sadkane [1998].…”