  (Abridged) We study the impact of cluster environment on the evolution of
spiral galaxies by examining their structure and kinematics. Rather than
two-dimensional rotation curves, we observe complete velocity fields by placing
three adjacent and parallel FORS2 MXU slits on each object, yielding several
emission and absorption lines. The gas velocity fields are reconstructed and
decomposed into circular rotation and irregular motions using kinemetry. To
quantify irregularities in the gas kinematics, we define three parameters:
sigma_{PA} (standard deviation of the kinematic position angle), Delta phi (the
average misalignment between kinematic and photometric position angles) and
k_{3,5} (squared sum of the higher order Fourier terms). Using local,
undistorted galaxies from SINGS, these can be used to establish the regularity
of the gas velocity fields. Here we present the analysis of 22 distant galaxies
in the MS0451.6-0305 field with 11 members at z=0.54. In this sample we find
both field (4 out of 8) and cluster (3 out of 4) galaxies with velocity fields
that are both irregular and asymmetric. We show that these fractions are
underestimates of the actual number of galaxies with irregular velocity fields.
The values of the (ir)regularity parameters for cluster galaxies are not very
different from those of the field galaxies, implying that there are isolated
field galaxies that are as distorted as the cluster members. None of the
deviations in our small sample correlate with photometric/structural properties
like luminosity or disk scale length in a significant way.
  Our 3D-spectroscopic method successfully maps the velocity field of distant
galaxies, enabling the importance and efficiency of cluster specific
interactions to be assessed quantitatively.
