  Spirals have been studied from a dynamical system perspective starting with
Barkley's seminal papers linking a wide class of spiral wave dynamics to the
Euclidean symmetry of the excitable media in which they are observed. However,
in order to explain certain non-Euclidean phenomena, such as anchoring and
epicyclic drifting, LeBlanc and Wulff introduced a single translational
symmetry-breaking perturbation to the center bundle equation and showed that
rotating waves may be attracted to a non-trivial solution manifold and travel
epicyclically around the perturbation center.
  In this paper, we continue the (model-independent) investigation of the
effects of inhomogeneities on spiral wave dynamics by studying epicyclic
drifting in the presence of: a) $n$ simultaneous translational
symmetry-breaking terms, with $n > 1$, and b) a combination of a single
rotational symmetry-breaking term and a single translational symmetry-breaking
term. These types of forced Euclidean symmetry-breaking provide a much more
realistic model of certain excitable media such as cardiac tissue. However, the
main theoretical tool used by LeBlanc and Wulff can only be applied to their
particular perturbation: we show how an averaging theorem of Hale can be
modified to analyze our two more general scenarios and state the conditions
under which epicyclic drifting takes place in the general case. In the process,
we recover LeBlanc and Wulff's specific result. Finally, we illustrate our
results with the help of a simple numerical simulation of a modified bidomain
model.
