  Equations of a heavy rotating body with one fixed point can be deduced
starting from a variational problem with holonomic constraints. When applying
this formalism to the particular case of a Lagrange top, in the formulation
with a diagonal inertia tensor the potential energy has more complicated form
as compared with that assumed in the literature on dynamics of a rigid body.
This implies the corresponding improvements in equations of motion. Therefore,
we revised this case, presenting several examples of analytical solutions to
the improved equations. The case of precession without nutation has a
surprisingly rich relationship between the rotation and precession rates, and
this is discussed in detail.
