  This paper considers uncertainty quantification in systems perturbed by
stochastic disturbances, in particular, Gaussian white noise. The main focus of
this work is on describing the time evolution of statistical moments of certain
invariants (for instance total energy and magnitude of angular momentum) for
such systems. A first case study for the attitude dynamics of a rigid body is
presented where it is shown that these techniques offer a closed form
representation of the evolution of the first and second moments of the kinetic
energy of the resulting stochastic dynamical system. A second case study of a
two body problem is presented in which bounds on the first and second moments
of the angular momentum are presented.
