Inverse eigenvalue problems for discrete gyroscopic systems

A discrete gyroscopic system is characterized by first-order ordinary differential equations defined by one symmetric and one skew-symmetric, which system describes the motion of a spinning body containing elastic parts. In this paper, we consider the inverse problems of such system: Given partial spectral data, find a system such that it is of the desired spectral data. The general solution of the problem is given and the best approximation solution to a pair of matrices is provided by QR-decomposition and matrix derivation. In addition, we also consider a special case in which the system operates below the lowest critical speed. The numerical examples show that the proposed method is effective.