# твердое тело

## The Stabilization of Program Motions of Firm Body on a Moving Platform

We consider ﬁrm body with ﬁxed point on a moving 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 Lyapunov’s functions having constant signs derivatives.

## Movement of a Firm Body With a Liquid of Small Viscosity

On the basis of the approach F.L. Tchernousko the equations in the integro-differential form of spatial movement of a body with a cavity wholly ﬁlled liquid of small viscosity are received. For a special case of movement the integro-differential equation is shown to ordinary differential, and with the help of a method of averaging the approached analytical decision is received. The examples showing accuracy of the received decision and inﬂuence of parameters of system on its movement are given.

## Solving Kinematic Problem of Optimal Nonlinear Stabilization of Arbitrary Program Movement of Free Rigid Body

The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values.