  We study occurrence of chaos in a four-mirror optomechanical cavity with
mechanical drives externally interacting with two transversely located
moving-end mirrors of the cavity. The strong cavity mode, driven by the pump
laser, excites mechanical oscillations in both moving-end mirrors with its
radiation pressure. These radiation-pressure-induced mechanical effects then
lead to the indirect coupling between two transverse mirrors, where
intra-cavity field mimics as a spring between two mechanical objects. By
computing Poincar\'e surface of sections for both mirrors over a wide interval
of initial conditions, we illustrate the transition from stable to mixed --
containing stable islands and chaotic seas -- Poincar\'e surface of sections
with external mechanical drives. To further explore the occurrence of chaos
with mechanical drives, we measure the spatio-temporal responses of moving-end
mirrors initially located in mixed Poincar\'e sections. We find that both of
the mirrors follow chaotic temporal evolution with external mechanical drives,
even in the absence of any one of the mechanical drives. To quantitatively
measure the occurrence of chaos, we computed the possible Lyapunov exponents
and collective Kolmogorov-Sinai Entropy of the system. We find that the largest
Lyapunov exponent, and corresponding Kolmogorov-Sinai Entropy, not only gains
positive values with increase in external drives but also crucially depends on
the initial conditions chosen from the Poincar\'e surface of sections.
Furthermore, we show the enhancement in chaotic dynamics of mirrors in the
presence of mechanical damping rates associated with the oscillatory motion of
the mirrors.
