Using Galactic dynamics we have determined the age of the low-mass post-T Tauri stars in the TW Hya Association (TWA). To do so we applied the method of Ortega and coworkers to five stars of the association with Hipparcos-measured distances (TWA 1, TWA 4, TWA 9, TWA 11, and TWA 19). The method is based on the calculation of the past three-dimensional orbits of the stars. Of these stars, only TWA 9 presents a quite different orbit so that it does not appear to be a dynamical member of the TWA. The four remaining stars have their first maximum orbital confinement at the age of -8.3±0.8 Myr, which is considered the dynamical age of the TWA. This confinement fixes the probable three-dimensional forming region of the TWA within a mean radius of 14.5 pc. This region is related to the older subgroups of the Sco-Cen OB association, Lower Centaurus Crux and Upper Centaurus Lupus, both with a mean age of about 18 Myr. This dynamical age of the TWA and that of the β Pic Moving Group, 11 Myr, also discussed here, introduce a more precise temporal scale for studies of disk evolution and planetary formation around some stars of these associations. Using the retraced orbit of the runaway star HIP 82868 we examine the possibility that the formation of the TWA was triggered by a supernova explosion. It is shown that for the four considered TWA stars, the expansion in volume is a factor of 5 from their origin to the present state. This is mainly due to the currently more distant star TWA 19.