  Various actuators are used in spacecraft to achieve attitude stabilization,
including thrusters, momentum wheels, and control moment gyros. Small
satellites, however, have stringent size, weight, and cost constraints, which
makes many actuator choices prohibitive. Consequently, magnetic torquers have
commonly been applied to spacecraft to attenuate angular rates. Approaches for
dealing with under-actuation due to magnetic control torque's dependency on the
magnetic field and required high magnetic flux densities have been previously
considered. Generally speaking, control of a satellite that becomes
under-actuated as a result of on-board failures has been a recurrent theme in
the literature. Methods for controlling spacecraft with fewer actuators than
degrees of freedom are increasingly in demand due to the increased number of
small satellite launches. Magnetic torquers have been extensively investigated
for momentum management of spacecraft with momentum wheels and for nutation
damping of spin satellites, momentum-biased, and dual-spin satellites.
Nonetheless, severely under-actuated small spacecraft that carry only a
single-axis magnetic torquer have not been previously treated. This note
considers the detumbling of a small spacecraft using only a single-axis
magnetic torquer. Even with a three-axis magnetic torquer, the spacecraft is
under-actuated, while, in the case of only a single axis magnetic torquer, the
problem is considerably more demanding. Our note examines the feasibility of
spacecraft attitude control with a single-axis magnetic torquer and possible
control methods that can be used.
