SPECS 2004 Operations Triangle Formation Possible formation control

SPECS 2004 Operations: Triangle Formation Possible formation control scenario with triangle formation Where is wheel speed, is combined spacecraft (MSC+CSC) angular velocity, is angular velocity of CSC, and is angular velocity of 3 MSC in formation 1). Initially 3 -axis controlled, prior to first observation: 2). External attitude control thrusters fire for momentum dump: after this maneuver, define initial angular momentum state, 3). Angular momentum of system described by: where is moment of inertia of MSC+CSC, containing axial moments of inertia of wheels, and wheel orientation. With specify a such that is matrix describes and the mass properties given, becomes the desired initial value:

SPECS 2004 Operations: Triangle Formation Possible formation control scenario with triangle formation (cont. ) 4). MSC separate and tethers begin to reel out, where inertia of the 3 MSC, increases with time, and the inertia of CSC, remains constant. Momentum of system remains constant, thus: where is the momentum of the CSC and is the momentum of the MSC group, yielding: 5). When comparing the momentum of the CSC before and after the instant of release: Before: After:

SPECS 2004 Operations: Triangle Formation Control scenario of triangle formation 1). Consider the formation (CSC+3*MSC) rigidly attached initially, with total moment of inertia and initial angular momentum 2). Now consider the formation after separation, where the moment of inertia of just the CSC is and the moment of inertia of the 3 MSC plus tethers is The angular momentum of the system is now where is the angular momentum of the CSC and is the angular momentum of the MSC group.