  Considerable research has led to ergodic isothermal dynamics which can
replicate Gibbs' canonical distribution for simple ( small ) dynamical
problems. Adding one or two thermostat forces to the Hamiltonian motion
equations can give an ergodic isothermal dynamics to a harmonic oscillator, to
a quartic oscillator, and even to the "Mexican-Hat" ( double-well ) potential
problem. We consider here a time-reversible dynamical approach to Gibbs'
"microcanonical" ( isoenergetic ) distribution for simple systems. To enable
isoenergetic ergodicity we add occasional random rotations to the velocities.
This idea conserves energy exactly and can be made to cover the entire energy
shell with an ergodic dynamics. We entirely avoid the Poincar\'e-section holes
and island chains typical of Hamiltonian chaos. We illustrate this idea for the
simplest possible two-dimensional example, a single particle moving in a
periodic square-lattice array of scatterers, the "cell model".
