The book deals with the model problems of the dynamics of solids, in relation to the bodies of heaven and earth. Special attention is paid to the combination of regularity and randomness of the movement. From this point of view, the dynamics of the body of a bipedal apparatus is described; the problems of orientation and stabilization of artificial and natural celestial bodies; the foundations of the theory of dynamic billiards in the gravitational field The last section of the book contains a brief overview of the author's most important results in long-term (since 1956) studies of the problems of rotational motions of celestial bodies, including Cassini's "generalized laws" of resonant rotational motions of celestial bodies. The book contains a large number of drawings showing a combination of regular and chaotic trajectories in the phase space.