  Equations of a rotating body with one point constrained to move freely on a
plane (dancing top) are deduced from the Lagrangian variational problem. They
formally look like the Euler-Poisson equations of a heavy body with fixed
point, immersed in a fictitious gravity field. Using this analogy, we have
found examples of analytical solutions for the case of a heavy symmetrical
dancing top. They describe the motions with center of mass keeping its height
fixed above the supporting plane. General solution to equations of a dancing
top in terms of exponential of Hamiltonian field is given. An extra constraint,
that take into account the reaction of supporting plane, leads to modification
of the canonical Poisson structure and therefore the integrability according to
Liouville is under the question.
