Characterizing the reachable set for a spacecraft with two rotors

One commonly employed actuation device to change the orientation and angular velocity of a satellite is the reaction wheel (or internal rotor.) With this mode of actuation, to achieve any arbitrary orientation and angular velocity, three internal rotors suffice. A problem of long standing interest however, is the aspect of controllability when there are only two rotors - either by design or due to the failure of one rotor. An early result on this problem is by Crouch [1]. The paper affirms that the system is not accessible when there are two rotors. However, there is no attempt to characterize the reachable set in this case. In this paper, using a geometric framework based on the Lagrange -Routh reduction procedure, we characterize the reachable set for the case of two rotors.