  Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic
analysis and representation theory of the algebra of functions on the quantum
group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role
of special states on the quantum algebra in an investigation of the
semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl
quantization and a relavence of contact geometry in this context is pointed
out. Dynamics on the quantum group parametrized by a real time variable and
corresponding to classical rotations is considered.
