Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB14

This note discusses the stability of collinear equilibrium points around a rotating system composed of two masses rigidly connected by a massless rod in the case, where the centripetal force outweighs the gravitational force. It is found that a stable region appears at L 1 when the ratio of gravitational to centripetal acceleration is less than 0.125, and that there is always no stable area at L 2 and L 3 ; the result is applied to the fast rotating Asteroid 2000EB14.