Quadratic inverse eigenvalue problem for damped gyroscopic systems

In this paper, we discuss the quadratic inverse eigenvalue problem for damped gyroscopic systems, that is, we are to construct a damped gyroscopic second order system having given $2n$ eigenvalues and associated eigenvectors as its full eigenstructure. Under some mild assumptions, the coefficient matrices are constructed in a recursive process. We also discuss how to obtain a damped gyroscopic system with the leading coefficient matrix $M$ being positive definite.