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It was proposed the Lie group such that symplectic structure of orbits ofco-adjoint representation of the group is revealed symplectic structure of arigid body dynamics in quaternion variables. It is shown that Poisson bracketsof corresponding Lie-Poisson structure coincide with canonical Poisson bracketson cotangent bundle of group unit quaternions.

Quaternions in Hamiltonian dynamics of a rigid body -- Part II. Relation of canonical Poisson and Lie-Poisson structures