Speaker : Nawaf M. Bou-Rabee Applied & Computational Mathematics, Caltech

Title: Tippe Top Inversion as a Dissipation-Induced Instability

In this talk I will show that tippe top inversion is fully described by a normal form for rotationally symmetric planar dynamical systems: the modified Maxwell-Bloch equations. Tippe top inversion occurs when a standard top with a blunt end rises from a gravitationally favorable position to an unfavorable one because of gyroscopic/dissipative effects. I will begin with a discussion of the mathematical model followed by a local/global analysis of the equations of motion for the tippe top. This standard analysis reveals that: (i) the modified Maxwell-Bloch equations fully describe tippe top inversion and (ii) they are the simplest possible equations that can capture the phenomenon. For more information please visit: http://www.acm.caltech.edu/~nawaf/tippetop.html