  We devise a generalisation of the energy momentum-method for studying the
stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian
symmetries. A generalisation of the relative equilibrium point notion to a
non-autonomous realm is provided and studied. Relative equilibrium points of
non-autonomous Hamiltonian systems are described via foliated Lie systems,
which opens a new field of application of such differential equations. We
reduce non-autonomous Hamiltonian systems via the Marsden-Weinstein theorem and
we provide conditions ensuring the stability of the projection of relative
equilibrium points to the reduced space. As an application, we study the
stability of relative equilibrium points for a class of mechanical systems,
which covers rigid bodies as a particular instance.
