  Strongly interacting particles in one dimension subject to external
confinement have become a topic of considerable interest due to recent
experimental advances and the development of new theoretical methods to attack
such systems. In the case of equal mass fermions or bosons with two or more
internal degrees of freedom, one can map the problem onto the well-known
Heisenberg spin models. However, many interesting physical systems contain
mixtures of particles with different masses. Therefore, a generalization of the
recent strong-coupling techniques would be highly desirable. This is
particularly important since such problems are generally considered
non-integrable and thus the hugely successful Bethe ansatz approach cannot be
applied. Here we discuss some initial steps towards this goal by investigating
small ensembles of one-dimensional harmonically trapped particles where
pairwise interactions are either vanishing or infinitely strong with focus on
the mass-imbalanced case. We discuss a (semi)-analytical approach to describe
systems using hyperspherical coordinates where the interaction is effectively
decoupled from the trapping potential. As an illustrative example we analyze
mass-imbalanced four-particle two-species mixtures with strong interactions
between the two species. For such systems we calculate the energies, densities
and pair-correlation functions.
