SE-581 83, Linkoeping, Sweden
Department of Mathematics, Linkoepings Universitet
Rauch-Wojciechowski S., Skoeldstam M., Glad T.
Mathematical analysis of the tippe top
2005, vol. 10, no. 4, pp. 333-362
A rigorous, and possibly complete analysis of the phase space picture of the tippe top solutions for all initial conditions when the top does not jump and all relations between parameters $\alpha$ and $\gamma$, is for the first time presented here. It is based on the use the Jellett's integral of motion $\lambda$ and the analysis of the energy function. Theorems about stability and attractivity of the asymptotic manifold are proved in detail. Lyapunov stability of (periodic) asymptotic solutions with respect to arbitrary perturbations is shown.