Vibratory mechanism can make the experimental model produce simple oscillatory movement and simple swinging movement.

Bifurcation of periodic motion on frequency in nonlinear vibration mechanism with piece-wise linearity;

he paper is concerned with the stability of the springless vibrohammer periodic motion with one shock per period.

Bifurcation and chaos of periodic motions of a single-degree-of-freedom system with piecewise-linearity is studied.

Then the Poincaré map of its period motion is established by utilizing the stability theory of system with periodic coefficients.

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

The Poincar map of the period motion is established following the Floquet theory .

Stationary motions of the system were determined and periodic motions near them are conustructed using the Liapounov theorem of the holomorphic integral.

We obtain some theorem on stability, boundedness,existence of periodic motions and stationary oscillation by means of the method of Lyapunov function.

We obtain some theorems on stability, boundedness, existence of periodic motions and stationary oscillation by means of the method of Lyapunov functional.