Construction of the programmed motion of double pendulum of variable length with fixed point of suspension

In this article the problem of constructing asymptotically stability arbitrarily given program motions of the double pendulum of variable length with a moving point of suspension is solved. The solution is obtained by synthesis of the active program control applied to the system of bodies, and the stabilizing control on the principle of feedback. Control is done in the form of an exact analytical solution in the class of continuous functions. The problem is solved by direct method of Lyapunov stability theory with Lyapunov's functions with constant sign of the derivatives.