1 Department of Mathematics, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Department of Applied Engineering Design and Production, Technical University of Denmark4 unknown
A large class of rotor systems can be modelled by a complex matrix differential equation of secondorder. The angular velocity of the rotor plays the role of a parameter. We apply the Lyapunov matrix equation in a complex setting and prove two new stability results which are compared with the results of the classical approach using Rayleighquotients. Several rotor systems are tested: a simple Laval rotor, a Laval rotor with additional elasticity and damping in thr bearings, and a number of rotor systems with complex symmetric 4x4 randomly generated matrices.