  Many processes within galaxy clusters, such as those believed to govern the
onset of thermally unstable cooling and AGN feedback, are dependent upon local
dynamical timescales. However, accurately mapping the mass distribution within
individual clusters is challenging, particularly towards cluster centres where
the total mass budget has substantial radially-dependent contributions from the
stellar, gas, and dark matter components. In this paper we use a small sample
of galaxy clusters with deep Chandra observations and good ancillary tracers of
their gravitating mass at both large and small radii to develop a method for
determining mass profiles that span a wide radial range and extend down into
the central galaxy. We also consider potential observational pitfalls in
understanding cooling in hot cluster atmospheres, and find tentative evidence
for a relationship between the radial extent of cooling X-ray gas and nebular
H-alpha emission in cool core clusters. Amongst this small sample we find no
support for the existence of a central 'entropy floor', with the entropy
profiles following a power-law profile down to our resolution limit.
