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

[摘要] Givenkpairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructingn×nreal matricesM,D,G, andK, whereM>0,KandDare symmetric, andGis skew-symmetric, so that the quadratic pencilQ(λ)=λ2M+λ(D+G)+Khas the givenkpairs as eigenpairs. First, we construct a general solution to this problem withk≤n. Then, with the special propertiesD=0andK<0, we construct a particular solution. Numerical results illustrate these solutions.

[学科分类] 应用数学