  We analyze the classical dynamics of a system composed of a one-dimensional
cavity with a perfect, fixed mirror and a movable mirror with non-zero
transparency interacting with a monochromatic laser. The movable mirror can
deviate far from an equilibrium position, it is assumed to be thin so that it
is modelled by a delta function, and we use the exact modes of the complete
system. The transparency and the mirror-position dependent cavity resonance
frequencies are built into the modes and this allows us to deduce that the
radiation pressure force comes from a periodic potential with period half the
wavelength of the field. The exact modes and the radiation pressure potential
allow us to give intuitive physical interpretations of the dynamics of the
system and to obtain approximate analytic solutions for the motion of the
mirror. Three regimes are identified depending on the intensity of the field
and it is found that the dynamics can be qualitatively very different in each
of them with some regimes being very sensitive to the values of the parameters.
Moreover, we determine conditions when the Maxwell-Newton equations used to
describe the system constitute accurate approximations of the exact equations
governing the dynamics.
