Abstract:
A fast rotating tippe top (TT) defies our intuition because, when it is launched on its bottom, it flips over to spin on its handle. The existing understanding of the flipping motion of TT is based on analysis of stability of asymptotic solutions for different values of TT parameters: the eccentricity of the center of mass $0 \leq \alpha \leq 1$ and the quotient of main moments of inertia $\gamma = I_1 / I_3$. These results provide conditions for flipping of TT but they say little about dynamics of inversion.
I propose here a new approach to study the equations of TT and introduce a Main Equation for the tippe top. This equation enables analysis of dynamics of TT and explains how the axis of symmetry $\hat{3}$ of TT moves on the unit sphere $ S^2 $. This approach also makes possible to study the relationship between behavior of TT and the law of friction.
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