Possible formation control scenario with triangle formation

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SPECS 2004 Operations Triangle Formation
Possible formation control scenario with triangle
formation Where is wheel speed, is
combined spacecraft (MSCCSC) 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 MSCCSC,
is matrix containing axial moments of
inertia of wheels, and describes wheel
orientation. With and the mass
properties given, specify a such that
becomes the desired initial value
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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
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SPECS 2004 Operations Triangle Formation
Control scenario of triangle formation
1). Consider the formation (CSC3MSC) 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.