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

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.