The stabilization of program motions of firm body on a moving platform

We consider firmbody with fixed point on amoving platform.We solve the problem of construction asimptotically stability programm motion. The programm motion can be any function. Control is received in the form the analytical solution. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunovs functions having constant signs derivatives.