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- W2731746042 abstract "This thesis deals with systems of the form(Mddot x+Ddot x+Kx=0;, ; x in mathbb R^n;,)with a positive definite mass matrix (M), a symmetric damping matrix (D) and a positive definite stiffnessmatrix (K). If the equilibrium in the system is unstable, a small disturbance is enough to set the system in motion again. The motion of the system sustains itself, an effect which is called self-excitation or self-induced vibration. The reason behind this effect is the presence of negative damping, which results for example from dry friction. Negative damping implies that the damping matrix (D) is indefinite or negative definite. Throughout our work, we assume (D) to be indefinite, and that the system possesses both stable and unstable modes and thus is unstable.It is now the idea of gyroscopic stabilization to mix the modes of a system with indefinite damping suchthat the system is stabilized without introducing furtherdissipation. This is done by adding gyroscopic forces (Gdot x) with a suitableskew-symmetric matrix (G) to the left-hand side. We call (G=-G^Tinmathbb R^{ntimes n}) a gyroscopic stabilizer forthe unstable system, if (Mddot x+(D+ G)dot x+Kx=0)is asymptotically stable. We show the existence of (G) in space dimensions three and four." @default.
- W2731746042 created "2017-07-14" @default.
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- W2731746042 date "2012-01-01" @default.
- W2731746042 modified "2023-09-24" @default.
- W2731746042 title "On Gyroscopic Stabilization" @default.
- W2731746042 hasPublicationYear "2012" @default.
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