Attitude determination and stabilization of a spherically
symmetric rigid body in a magnetic field
Abstract
Observation and stabilization problems for a rigid body
rotating about its mass centre in a time-periodic magnetic
field is considered. The moment of the applied forces about the
mass centre is a vector product of the field and the vector of
control. The only measurement is of the field and its time
derivatives is the body co-ordinates. The model describes the
angular motion of a satellite in the geomagnetic field with the
control carried out by a magnetic moment of current coils
(magnetorquers) mounted on the satellite body. It is shown that
generically the knowledge of the field and its derivatives is
sufficient for the attitude determination. A problem of
stabilization along one direction is considered. The stabilizer
constructed in this work drives the system to a given motion
from all initial points that do not belong to an unstable
manifold. It is shown that all stabilizers have such a manifold
of initial conditions.