  Flows forced by a precessional motion can exhibit instabilities of crucial
importance, whether they concern the fuel of a flying object or the liquid core
of a telluric planet. So far, stability analyses of these flows have focused on
the special case of a resonant forcing. Here, we address the instability of the
flow inside a precessing cylinder in the general case. We first show that the
base flow forced by the cylinder precession is a superposition of a vertical or
horizontal shear flow and an infinite sum of forced modes. We then perform a
linear stability analysis of this base flow by considering its triadic
resonance with two free Kelvin modes. Finally, we derive the amplitude
equations of the free Kelvin modes and obtain an expression of the instability
threshold and growth rate.
