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

Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutions