A solution of the eigenproblem for undamped gyroscopic systems with the Lanczos algorithm

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Abstract
This paper presents an efficient numerical solution of the quadratic eigenproblem arising in the analysis of gyroscopic systems. Such problems are known to reduce to a generalized linear eigenproblem defined by two real non‐singular matrices, one symmetric and one skew‐symmetric. For this class of problems, the general Lanczos algorithm for unsymmetric matrices is shown to simplify considerably and yields an efficient solution of the problem. Full advantage can be taken of the sparsity of the matrices and of the specific nature of gyroscopic systems. Numerical examples are presented, which demonstrate the efficiency and accuracy of the solution procedure.