  The dynamics of Fabry-Perot cavity with suspended mirrors is described. The
suspended mirrors are nonlinear oscillators interacting with each other through
the laser circulating in the cavity. The degrees of freedom decouple in normal
coordinates, which are the position of the center of mass and the length of the
cavity. We introduce two parameters and study how the dynamics changes with
respect to these parameters. The first parameter specifies how strong the
radiation pressure is. It determines whether the cavity is multistable or not.
The second parameter is the control parameter, which determines location of the
cavity equilibrium states. The equilibrium state shows hysteresis if the
control parameter varies within a wide range. We analyze stability of the
equilibrium states and identify the instability region. The instability is
explained in terms of the effective potential: the stable states correspond to
local minima of the effective potential and unstable states correspond to local
maxima. The minima of the effective potential defines the resonant frequencies
for the oscillations of the cavity length. We find the frequencies, and analyze
how to tune them. Multistability of the cavity with a feedback control system
is analyzed in terms of the servo potential. The results obtained in this paper
are general and apply to all Fabry-Perot cavities with suspended mirrors.
