An inverse eigenvalue problem for damped gyroscopic second-order systems (Q1036444)

Summary: The inverse eigenvalue problem of constructing a symmetric positive semidefinite matrix \(D\) (written as \(D\geq 0)\) and a real-valued skew-symmetric matrix \(G\) (i.e., \(G^{T}= - G\)) of order \(n\) for the quadratic pencil \(Q(\lambda ):=\lambda ^{2}M_{a}+\lambda (D+G)+K_{a}\), where \(M_{a}>0, K_{a}\geq 0\) are given analytical mass and stiffness matrices, so that \(Q(\lambda )\) has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are specified.