On Linearization of Mechanical Control Systems

We discuss linearization, via a diffeomorphism, of mechanical control systems and study the problem of whether both structures, linear and mechanical ones, are compatible. The first problem we consider is: given a mechanical control systems that is linearizable, can we linearize it preserving, simultaneously, its given mechanical structure. The second problem is whether a general control-affine system that is linearizable and admits a mechanical control structure can be transformed into a linear mechanical structure. Finally we discuss equivalence to a subclass of linear mechanical control systems, namely those subject to positional forces only.