| Summary: | The equations of motion for a multibody tethered satellite system in three dimensional
Keplerian orbit are derived. The model considers a multi-satellite system
connected in series by flexible tethers. Both tethers and subsatellites are free to undergo
three dimensional attitude motion, together with deployment and retrieval as
well as longitudinal and transverse vibration for the tether. The elastic deformations
of the tethers are discretized using the assumed mode method. The tether attachment
points to the subsatellites are kept arbitrary and time varying. The model is also capable
of simulating the response of the entire system spinning about an arbitrary
axis, as in the case of OEDIPUS-A/C which spins about the nominal tether length,
or the proposed BICEPS mission where the system cartwheels about the orbit normal.
The governing equations of motion are derived using a non-recursive order(N)
Lagrangian procedure which significantly reduces the computational cost associated
with the inversion of the mass matrix, an important consideration for multi-satellite
systems. Also, a symbolic integration and coding package is used to evaluate modal
integrals thus avoiding their costly on-line numerical evaluation.
Next, versatility of the formulation is illustrated through its application to
two different tethered satellite systems of contemporary interest. Finally, a thruster
and momentum-wheel based attitude controller is developed using the Feedback Linearization
Technique, in conjunction with an offset (tether attachment point) control
strategy for the suppression of the tether's vibratory motion using the optimal Linear
Quadratic Gaussian-Loop Transfer Recovery method. Both the controllers are
successful in stabilizing the system over a range of mission profiles.
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