Maybe there is something more complicated going on with helicopters that I am not aware of, but a helicopter would not be an inherently stable system due to it "hanging" from the rotor because the direction the rotors are providing thrust changes (all other things being equal), when the helicopter starts to tip one direction.
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Agreed, though the one leg analogy would more accurately be hanging from one arm, since the lift is provided from above.
Ehhh... that sounds like an example of the rocket pendulum fallacy: http://en.wikipedia.org/wiki/Pendulum_rocket_fallacy
Maybe there is something more complicated going on with helicopters that I am not aware of, but a helicopter would not be an inherently stable system due to it "hanging" from the rotor because the direction the rotors are providing thrust changes (all other things being equal), when the helicopter starts to tip one direction.
Seems you're right, though I think it would depend on the rigidity of the rotor with respect to the body of the helicopter.