Two configurations for a unicycle, a class of nonholonomic systems, is looked into. The first configuration is the case where the generalized coordinates consists of four parameters, while the other configurations consists of five. For both systems the equations of motion are calculated. Then a method for parameterizing a desired path for the systems using a synchronization function among all degrees of freedom is shown. A set of equations to find feasible trajectories keeping the desired path virtually constrained is calculated. It is then shown for the four degree of freedom system how to compute the transverse linearization, which can be used for orbital stabilization of a desired motion consisting of circular orbits or straight paths. A way to compute a periodic controller for a linear time varying system is derived, and a set of controllers are tried out on the four degree of freedom unicycle with negative result.