On nonlinear control of the Ishlinsky system as an example of a nonholonomic non-Chaplygin system

We consider a control problem for a nonholonomic non-Chaplygin mechanical system. The specific example, which we refer to as the Ishlinsky example, involves maneuvering of a single cylinder which rolls on top of two identical cylinders, each rolls on a horizontal plane. We formulate and analyze controllability conditions for the system of cylinders. This example of a non-Chaplygin system illustrates the analytic and control complexity of such problems. One feature of this complexity is that the controllability properties are strongly local. Symbolic computations using Mathematica are employed to obtain up to level three Lie brackets that expose these controllability properties at selected configurations