Harmonic disturbance in a controlled mechanical system with friction

The controlled motions of a mechanical system under dry and viscous friction and a disturbing harmonic force are investigated. The time optimal control function for the undisturbed point-to-point problem is applied to the system. The resulted trajectories and periodic limiting motions with different system parameters are investigated. The emergence and stability conditions of the simple cycles are analyzed. For the disturbed system the synthesis and program law of the time optimal control were derived. It was shown for each acceptable set of parameters that there exists a piecewise constant optimal control with no more than one switch.