Solutions of a quadratic inverse eigenvalue problem for damped gyroscopic second-order systems (Q1714717)

Summary: Given \(k\) pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing \(n\times n\) real matrices \(M\), \(D\), \(G\), and \(K\), where \(M>0\), \(K\) and \(D\) are symmetric, and \(G\) is skew-symmetric, so that the quadratic pencil \(Q(\lambda)=\lambda^2 M + \lambda(D+G) + K\) has the given \(k\) pairs as eigenpairs. First, we construct a general solution to this problem with \(k\leq n\). Then, with the special properties \(D=0\) and \(K< 0\), we construct a particular solution. Numerical results illustrate these solutions.