I toiled late into the night last night trying to get this figured out (assymetric recovering forces)....I didn't have much luck.
If the line tension was constant, the restoring torque from the leadouts is
line tension*distance from CG to leadout guide*sin(yaw angle)
and just define a value K as the line tension*distance so you have a "coefficient of restoring force" , so for small angles this becomes:
K*yaw angle.
In unperturbed level flight for my airplane, say, the value of K is about 10 lbs*28" or about 280 in-lb/radian. But the line tension is a function of the yaw angle, too, and it goes down as the yaw angle goes negative (nose-in) and up as the yaw angle goes positive (nose-out). So, the K is not really a constant, but changes as the yaw angle changes- so the value of K goes down for nose-in yaw and up for nose-out yaw. For example say 9 lbs at some nose-in yaw angle, and 11 lb at some nose-out yaw angle. For the nose-in case K goes down to 252 in-lb/rad and the nose-out case it's 308. Asymmetrical.
Of course, if you knew how much the line tension changes as you change the yaw angle, you could put that function in where the line tension goes, have some function of the yaw angle and then simplify and get rid of the need for the "constant" K that isn't really a constant. In reality that isn't a known function - not because it's magical but because we just haven't worked it out. There are other restoring torques that aren't asymmetrical, like the fin/rudder and dihedral effects, and others that are not simple functions of the yaw angle (like, some of them have to to with the yaw rate and yaw angle past history) so to build up the entire equations of motion is a very difficult task.
Brett