  In classical mechanics, the 'geometry of motion' refers to a development to
visualize the motion of freely spinning bodies. In this paper, such an approach
of studying the rotational motion of axisymmetric variable mass systems is
developed. An analytic solution to the second Euler angle characterising
nutation naturally falls out of this method, without explicitly solving the
nonlinear differential equations of motion. This is used to examine the coning
motion of a free axisymmetric cylinder subject to three idealized models of
mass loss and new insight into their rotational stability is presented. It is
seen that the angular speeds for some configurations of these cylinders grow
without bounds. In spite of this phenomenon, all configurations explored here
are seen to exhibit nutational stability, a desirable property in solid rocket
motors.
