The collective coordinate treatment of mode coupling
in a beam plasma is investigated by computer simulation. Two methods are derived generalized and programmed. The
programming is done for a two mode, one species, stationary
plasma. The first method integrates the second order collective
Lagrangian equations for the mode amplitudes. This
method neglects the plasma temperature and coupling is not
observed. The second method integrates the first order
Hamiltonian equations for the mode amplitudes and their
canonical momentum. This takes account of the plasma temperature
and coupling is observed. A perturbation theory
approach is then suggested which would smooth out the detail
of the mode interactions and shorten the calculation time.