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 Denmark
This paper deals with gyroscopic stabilization of the unstable system Mx + D(x) over dot + K-x = 0, with positive definite mass and stiffness matrices M and K, respectively, and an indefinite damping matrix D. The main question if for which skew-symmetric matrices G the system Mx (D+ G)(x) over dot + K-x = 0 can become stable? After investigating special cases we find an appropriat solution of the Lyapunov matrix equation for the general case. Examples show the deviation of the stability limit found by the Lyapunov method from the exact value.
Zeitschrift Fuer Angewandte Mathematik Und Physik, 2009, Vol 60, Issue 4, p. 785-795