  Slitless spectroscopy has long been considered as a complicated and confused
technique. Nonetheless, with the advent of Hubble Space Telescope (HST)
instruments characterized by a low sky background level and a high spatial
resolution (most notably WFC3), slitless spectroscopy has become an adopted
survey tool to study galaxy evolution from space. We investigate its
application to single object studies to measure not only redshift and
integrated spectral features, but also spatially resolved quantities such as
galaxy kinematics. We build a complete forward model to be quantitatively
compared to actual slitless observations. This model depends on a simplified
thin cold disk galaxy description -- including flux distribution, intrinsic
spectrum and kinematic parameters -- and on the instrumental signature. It is
used to improve redshifts and constrain basic rotation curve parameters, i.e.
plateau velocity $v_{0}$ (in $\rm km.s^{-1}$) and central velocity gradient
$w_{0}$ (in $\rm km.s^{-1}.arcsec^{-1}$). The model is tested on selected
observations from 3D-HST and GLASS surveys, to estimate redshift and kinematic
parameters on several galaxies measured with one or more roll angles. Our
forward approach allows to mitigate the self-contamination effect, a primary
drawback of slitless spectroscopy, and therefore has the potential to increase
precision on redshifts. In a limited sample of well-resolved spiral galaxies
from HST surveys, it is possible to significantly constrain galaxy rotation
curve parameters. This proof-of-concept work is promising for future large
slitless spectroscopic surveys such as EUCLID and WFIRST.
