Nonlinear Dynamics of a Roller Bicycle

In this paper we consider the dynamics of a rollerbicycle on a horizontal plane. For this bicycle we derive anonlinear system of equations of motion in a form that allowsus to take into account the symmetry of the system in anatural form. We analyze in detail the stability of straight-linemotion 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.