Approximate constrained controllability of mechanical system

In the present paper approximate constrained controllability of linear abstract second-order infinite-dimensional dynamical control systems is considered. First, fundamental definitions and notions are recalled. Next it is proved, using the so-called frequency-domain method, that approximate constrained controllability of second-order dynamical control system can be verified by the approximate constrained controllability conditions for the simplified, suitably defined first-order linear dynamical control system. General results are then applied for approximate constrained controllability investigation of mechanical flexible structure vibratory dynamical system. Some special cases are also considered. Moreover, many remarks, comments and corollaries on the relationships between different concepts of approximate controllability are given. Finally, the obtained results are applied for investigation of approximate constrained controllability for flexible mechanical structure. In this case linear second-order partial differential state equation describes the transverse motion of an elastic beam which occupies the given finite interval.