  We present a dynamical model for the double torsion pendulum nicknamed PETER,
where one torsion pendulum hangs in cascade, but off-axis, from the other. The
dynamics of interest in these devices lies around the torsional resonance, that
is at very low frequencies (mHz). However, we find that, in order to properly
describe the forced motion of the pendulums, also other modes must be
considered, namely swinging and bouncing oscillations of the two suspended
masses, that resonate at higher frequencies (Hz). Although the system has
obviously 6+6 Degrees of Freedom, we find that 8 are sufficient for an accurate
description of the observed motion. This model produces reliable estimates of
the response to generic external disturbances and actuating forces or torques.
In particular, we compute the effect of seismic floor motion (tilt noise) on
the low frequency part of the signal spectra and show that it properly accounts
for most of the measured low frequency noise.
