Abstract
This paper describes the dynamics and impact model of a wheel with various radius rim. The dynamics is expressed by a rst order linear ordinary dierential equation with respect to the absolute orientation of the wheel, and an analytic solution is derived. Poincaré map is also derived analytically. Stability and basin of attraction (BoA) of the Poincaré map are discussed. Finally, the analysis is validated through some numerical simulations. As a result, the rim radius aects the stability and broadens its BoA. The analysis helps understanding of not only a geometric tracking control but also many underactuated control methods for bipeds.
