Controllability of mechanical systems in the class of controls bounded together with their derivatives

A series of studies concerned with controllability of the nonlinear dynamic mechanical systems such as manipulators, aircraft, or water-craft was continued. For the class of smooth controls which comprises swing-bounded controls with bounded derivatives, a criterion for controllability of mechanical systems was established in addition to the criterion for controllability in the class of bounded controls that was established earlier. The controllability criterion (necessary and sufficient conditions) was formulated for a set of mechanical systems, rather than for a particular system as usual. Stated differently, conditions for controllability of any system from the set were established. The elements of this set are represented by the systems obeying the Lagrange equations of the second kind and having also bounded inertial characteristics and generalized forces. The established controllability conditions have an obvious physical sense. For example, for a manipulation robot to be controllable, it is required that the control forces dominate over any other generalized forces such as weight or environmental resistance.Domination is necessary both in the amplitude of forces and rate of their variation, that is, the derivative.