In order to investigate the action of the galactic tide on the motion of the Oort cloud comets, a series of mappings are developed. These models are checked in three different frames, and some of them turn out to be reliable on a wide range of initial conditions. The transport of 105 Oort cloud comets to the inner Solar System is simulated, under the galactic tide impulse only. It is shown that for such simulation, the best compromise between reliability and computer time, is obtained by the mapping of order 3 which is 500 times faster than numerical integrations and is valid for cometary semi--major axes a < 30000 AU. The present study highlights the qualitative effects of the radial component of the galactic tide.