Chaos and its controlling of harmonically excited systems having rigid amplitude constraints

The complex dynamics characters of the two harmonically excited systems having rigid constraints with a clearance are studied. The dynamical equation and the state equation of the two systems are established. By the phase portraits, the motions of the systems are studied under the definite parameters. And by Poincaré map, the route from periodic motion to chaos is studied under the presented system parameters. The addition of constant motor torque is the best method to control chaos. This method directly adds a constant torque to the system to control the chaos of the system by adjusted the weight of the controlling parameter. The chaos of the system can be controlled so long as the appropriate value of the parameter is obtained. A group of phase plane portraits and time series of the controlled system are given in the paper through adjusting the value of the weight, u, of the additional constant. The orbits of the system can be controlled by the method according to the target.