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blochpresentation - Tippe Top Inversion as a...

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Tippe Top Inversion as a Dissipation-Induced Instability Advisor: Jerrold E. Marsden Nawaf M. Bou-Rabee Bloch’s Visit, 11/12/03
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Figure 1: L-R non-inverted and inverted tippe-top.
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Claim: Tippe top inversion is completely described by the modified Maxwell-Bloch equations.
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Dissipation-Induced Instability A dissipation-induced instability describes a neutrally stable equilibrium becoming spectrally (and hence nonlinearly) stable with the addition of dissipation. Potpourri of examples: motion of planets in celestial mechanics quasigeostrophic flow tubular cantilever conveying fluid rotating spherical pendulum (or bead on a rotating circular plate)
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History Dissipation-Induced Instabilities: (1994, Bloch, Krishnaprasad, Marsden, & Ratiu) analysis of phenomenon (2001, Clerc & Marsden) normal form for phenomenon (2002, Derks & Ratiu) effect of dissipation on families of relative equilibria in Hamiltonian systems
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History Tippe Top: (1905, Routh) commentary on rising of tops (1977, Cohen) numerical simulation of phenomenon (1994, Or) linear analysis of equations of motion (1995, Ebenfeld) orbital analysis of relative equilibria
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