  We explore the rotational stability of hovering flight. Our model is
motivated by an experimental pyramid-shaped object and a computational
lambda-shaped analog hovering passively in oscillating airflows; both systems
have been shown to maintain rotational balance during free flight. Here, we
attach the lambda-shaped flyer at its apex, allowing it to rotate freely akin
to a pendulum. We find that the flyer exhibits stable concave-down and
concave-up behavior. Importantly, the down and up configurations are bistable
and co-exist for a range of background flow properties. We explain the
aerodynamic origin of this bistability and compare it to the inertia-induced
stability of an inverted pendulum oscillating at its base. We then allow the
flyer to flap passively by introducing a rotational spring at its apex. For
stiff springs, flexibility diminishes upward stability but as stiffness
decreases, a new transition to upward stability is induced by flapping. We
conclude by commenting on the implications of these findings for biological and
man-made aircraft.
