  This work is devoted to a systematic exposition of the dynamics of a rigid
body, considered as a system with kinematic constraints. Having accepted the
variational problem in accordance with this, we no longer need any additional
postulates or assumptions about the behavior of the rigid body. All the basic
quantities and characteristics of a rigid body, as well as the equations of
motion and integrals of motion, are obtained from the variational problem by
direct and unequivocal calculations within the framework of standard methods of
classical mechanics. Several equivalent forms for the equations of motion of
rotational degrees of freedom are deduced and discussed on this basis. Using
the resulting formulation, we revise some cases of integrability, and discuss a
number of peculiar properties, that are not always taken into account when
formulating the laws of motion of a rigid body.
