When studying rotating fluid masses it was discovered in the nineteenth century that adding dissipation could destabilise the equilibria. This can be illustrated simpler by the rotating spherical bowl of H. Lamb and more generally by the rotating surface formulated by L.E.J. Brouwer; in the second case also the rotating saddle is included. An explication of the phenomena was presented by Bottema; this is also related to Arnold’s treatment of structural stability of matrices. An application in mechanics is given for a rotor system with external excitation.

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Instability Induced by Dissipation

  • Ferdinand Verhulst

摘要

When studying rotating fluid masses it was discovered in the nineteenth century that adding dissipation could destabilise the equilibria. This can be illustrated simpler by the rotating spherical bowl of H. Lamb and more generally by the rotating surface formulated by L.E.J. Brouwer; in the second case also the rotating saddle is included. An explication of the phenomena was presented by Bottema; this is also related to Arnold’s treatment of structural stability of matrices. An application in mechanics is given for a rotor system with external excitation.