1 Department of Mathematics, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark3 University of Wuppertal4 University of Wuppertal
The paper deals with linear systems of differential equationswith symmetric system matrices M,D, and K.The mass matrix M and the stiffness matrix K are both assumed to bepositive definite. The damping matrix D is indefinite. Three questionsare of interest: 1) When is the system unstable? Apparently not always,if the matrix D is indefinite. 2) What can we say about conditions whichensure that an unstable system can be stabilized by adding a gyroscopicterm Gdx/dt? 3) What is, in this case, a suitable or optimal matrixG? The questions are answered in the frame of a first order perturbationapproach.