Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium

Abstract

The dynamics of a mobile system with a movable internal mass is investigated in this paper. Due to the periodic motion of the internal acceleration-controlled mass as well as the anisotropy of the external resistance, the system can move in a resistive medium. Major attention is given to the steady-state motion and stick–slip effect of the system as a whole. For anisotropic Coulomb's dry friction, in light of the non-smooth factors in both the internal control mode and external resistance, method of averaging is adopted to obtain an approximate expression of the average steady-state velocity when the stick–slip motion is absent. Optimizing the parameters of the internal controlled mass enables one to realize a maximal average steady-state velocity of the system. In view of the stick–slip effect, the steady-state motion of the system is classified into eight types, and the characteristics of each type are analyzed. Stick–slip motion is of our interest and receives extra attention. Two strategies of control are put forward based on the characteristics of stick–slip motion. Making use of these two control strategies, directed motions of the system are possible and the direction of the motion can be simply controlled by modifying the values of internal accelerations. To achieve an always forward motion with higher average steady-state velocity, further optimization is carried out. For anisotropic linear resistance, the approximate expression of average steady-state velocity can be also obtained by the method of averaging. No stick–slip motion may occur in this instance. All the analytical results are numerically simulated in order to verify their correctness.