  We present a theoretical approach to study the dynamics of spherical,
cylindrical and ellipsoidal charge distributions under their self-Coulomb field
and a stochastic force due to collisions and random motions of charged
particles. The approach is based on finding the current density of the charge
distribution from the charge-current continuity equation and determining the
drift velocities of the particles. The latter can be used either to derive the
Lagrangian of the system, or to write Newtons equation of motion with the
Lorentz force. We develop a kinetic theory to include the stochastic force due
to random motions of electrons into our model. To demonstrate the efficacy of
our method, we apply it to various charge distributions and compare our results
to N-body simulations. We show that our method reproduces the well-known
emittance term in the envelope equation of uniform spherical and cylindrical
charge distributions with correct coefficients. We use our model for the
gravitational collapse of an ideal gas as well as the cyclotron dynamics of a
cylindrical charge distribution in a uniform magnetic field and propose a
method to measure the emittance of electron beams.
