Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems

Given k pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing n×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(λ)=λ2M+λ(D+G)+K has the given k pairs as eigenpairs. First, we construct a general solution to this problem with k≤n. Then, with the special properties D=0 and K<0, we construct a particular solution. Numerical results illustrate these solutions