  The evolution of rotation states of small asteroids is governed by the YORP
effect, nonetheless some asteroids can stop their YORP evolution by attaining a
stable equilibrium. The same is true for binary asteroids subjected to the
BYORP effect. Here we discuss a new type of equilibrium that combines these
two, which is possible in a singly synchronous binary system. This equilibrium
occurs when the normal YORP, the tangential YORP and the binary YORP compensate
each other, and tidal torques distribute the angular momentum between the
components of the system and dissipate energy. Such a system if unperturbed
would remain singly synchronous in perpetuity with constant spin and orbit
rates, as the tidal torques dissipate the incoming energy from impinging
sunlight at the same rate. The probability of the existence of this kind of
equilibrium in a binary system is found to be on the order of a few percent.
