Nonlinear Dynamics of a Roller Bicycle

In this paper we consider the dynamics of a roller bicycle on a horizontal plane. For this bicycle we derive a nonlinear system of equations of motion in a form that allows us to take into account the symmetry of the system in a natural form. We analyze in detail the stability of straight-line motion depending on the parameters of the bicycle. We find numerical evidence that, in addition to stable straight-line motion, the roller bicycle can exhibit other, more complex, trajectories for which the bicycle does not fall.