  We discuss an embedding of a vector field for the nonholonomic Routh sphere
into a subgroup of commuting Hamiltonian vector fields on six dimensional phase
space. The corresponding Poisson brackets are reduced to the canonical Poisson
brackets on the Lie algebra e(3). It allows us to relate nonholonomic Routh
system with the Hamiltonian system on cotangent bundle to the sphere with
canonical Poisson structure.
