  We investigate the velocity transition in the low-mass protostar L1489 IRS,
which is known to be embedded in a flattened, disc-like structure that shows
both infall and rotation. We construct a model for L1489 IRS consisting of an
flattened envelope and a velocity field that can vary from pure infall to pure
rotation. We obtain best-fit parameters by comparison to 24 molecular
transitions from the literature, and using a molecular excitation code and a
Voronoi optimisation algorithm. We test the model against existing millimeter
interferometric observations, near-infrared scattered light imaging, and 12CO
ro-vibrational lines.We find that L1489 IRS is well described by a central
stellar mass of 1.3M$_\odot$ surrounded by a 0.10M$_\odot$ flattened envelope
with approximate scale height h\approx 0.57 R, inclined at 74^\circ. The
velocity field is strongly dominated by rotation, with the velocity vector
making an angle of 15^\circ with the azimuthal direction. Reproducing
low-excitation transitions requires that the emission and absorption by the
starless core 1' (8400 AU) east of L1489 IRS is included properly, implying
that L1489 IRS is located partially behind this core. We speculate that L1489
IRS was originally formed closer to the center of this core, but has migrated
to its current position over the past few times 10^5 yr, consistent with their
radial velocity difference of 0.4 kms-1. This suggests that L1489 IRS' unusual
appearance may be result of its migration, and that it would appear as a
`normal' embedded protostar if it were still surrounded by an extended cloud
core. Conversely, we hypothesize that the inner envelopes of embedded
protostars resemble the rotating structure seen around L1489 IRS.
