  Detumbling refers to the act of dampening the angular velocity of the
satellite. This operation is of paramount importance since it is virtually
impossible to nominally perform any other operation without some degree of
attitude control. Common methods used to detumble satellites usually involve
magnetic actuation, paired with different types of sensors which are used to
provide angular velocity feedback. This paper presents the adverse effects of
time-discretization on the stability of two detumbling algorithms. An extensive
literature review revealed that both algorithms achieve absolute stability for
systems involving continuous feedback and output. However, the physical
components involved impose limitations on the maximum frequency of the
algorithm, thereby making any such system inconceivable. This asserts the need
to perform a discrete-time stability analysis, as it is better suited to
reflect on the actual implementation and dynamics of these algorithms. The
paper starts with the current theory and views on the stability of these
algorithms. The next sections describe the continuous and discrete-time
stability analysis performed by the team and the conclusions derived from it.
Theoretical investigation led to the discovery of multiple conditions on
angular velocity and operating frequencies of the hardware, for which the
algorithms were unstable. These results were then verified through various
simulations on MATLAB and Python3.6.7. The paper concludes with a discussion on
the various instabilities posed by time-discretization and the conditions under
which the detumbling algorithm would be infeasible.
