  The Poisson structure is constructed for a model in which spatial coordinates
of configuration space are noncommutative and satisfy the commutation relations
of a Lie algebra. The case is specialized to that of the group SU(2), for which
the counterpart of the angular momentum, as well as the Euler parameterization
of the phase space are introduced. SU(2)-invariant classical systems are
discussed, and it is observed that the path of particle can be obtained by the
solution of a first-order equation, as the case with such models on commutative
spaces. The examples of free particle, rotationally-invariant potentials, and
specially the isotropic harmonic oscillator are investigated in more detail.
