Chaotic Dynamics and Stability Analysis of a Roller Bicycle

We analyze the stability of the straight-line motion of the bicycle depending on the mass-geometric parameters of the bicycle and its translational velocity. We construct a region in phase space which corresponds to initial conditions under which the bicycle tends asymptotically to straight-line motion. To investigate the bifurcations of the periodic solutions of the system, we construct a chart of dynamical regimes on the plane of two parameters and a three-dimensional Poincaré map. We analyze the possibility of acceleration or deceleration of the bicycle when the angular velocity of the rotor periodically changes in time.