(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.
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