  We obtain by invariance arguments the relativistic and non-relativistic
invariant dynamical equations of a classical model of a spinning electron. We
apply the formalism to a particular classical model which satisfies Dirac's
equation when quantised. It is shown that the dynamics can be described in
terms of the evolution of the point charge which satisfies a fourth order
differential equation or, alternatively, as a system of second order
differential equations by describing the evolution of both the center of mass
and center of charge of the particle. As an application of the found dynamical
equations, the Coulomb interaction between two spinning electrons is
considered. We find from the classical viewpoint that these spinning electrons
can form bound states under suitable initial conditions. Since the classical
Coulomb interaction of two spinless point electrons does not allow for the
existence of bound states, it is the spin structure that gives rise to new
physical phenomena not described in the spinless case. Perhaps the paper may be
interesting from the mathematical point of view but not from the point of view
of physics.

Classical Physics;High Energy Physics - Theory;General Physics