  An algebraic procedure of getting of canonical variables in a rigid body
dynamics is presented. The method is based on using a structure of an algebra
of Lie-Poisson brackets with which a Hamiltonian dynamics is set. In a
particular case of a problem of a top in a homogeneous gravitation field the
method leads to well-known Andoyer-Deprit variables. Earlier, the method of
getting of them was based on geometric approach.
