A Mechanical Feedback Classification of Linear Mechanical Control Systems

We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space Rn only, while the state-space of a mechanical control system is Rn×Rn consisting of configurations and velocities.