  We derive Wong's equations for the finite-dimensional dynamical system
representing the motion of a scalar particle on a compact Riemannian manifold
with a given free isometric smooth action of a compact semisimple Lie group.
The obtained equations are written in terms of dependent coordinates which are
typically used in an implicit description of the local dynamics given on the
orbit space of the principal fiber bundle. Using these equations we obtain
Wong's equations in a pure Yang--Mills gauge theory with the Coulomb gauge
fixing. This result is based on the existing analogy between the reduction
procedures carried out in our finite-dimensional dynamical system and in
Yang-Mills gauge fields.
