Low-Order Controllability and Kinematic Reductions for Affine Connection Control Systems

Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, low-order controllability results are given for the class of mechanical control systems. Second, a precise connection is made between those mechanical systems which are dynamic (i.e., have forces as inputs) and those which are kinematic (i.e., have velocities as inputs). Interestingly and surprisingly, these two subjects are characterised and linked by a certain intrinsic vector-valued quadratic form that can be associated to an affine connection control system.