Sergey Gonchenko: On regular and chaotic dynamics of "celtic stone"

We study stable dynamics (both regular and chaotic) of the
well-known mechanical system "celtic stone" (called sometimes as "celt"
or "rattleback", or "wobblestone", or even "Russian stone"). Physically,
it is a canoe-shaped rigid body with the curious property of spin
asymmetry: it tends to have the stable vertical rotation in one
direction only, independently on initial conditions for rotation. In the
talk we try to explain this dynamical property by means of some
mathematical idealization - the nonholonomic model of celtic stone. We
study this model by numerical and qualitative methods and describe
various stable regimes: permanent rotation, oscillations and, finally,
chaotic dynamics.