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Quaternions in Hamiltonian dynamics of a rigid body -- Part II. Relation of canonical Poisson and Lie-Poisson structures (1508.04005v1)
Published 17 Aug 2015 in math-ph and math.MP
Abstract: It was proposed the Lie group such that symplectic structure of orbits of co-adjoint representation of the group is revealed symplectic structure of a rigid body dynamics in quaternion variables. It is shown that Poisson brackets of corresponding Lie-Poisson structure coincide with canonical Poisson brackets on cotangent bundle of group unit quaternions.