The trapping and sticking of H and D atoms on the graphite (0001) surface is examined over the energy range 0.1-0.9 eV. Total electronic energy calculations based on density functional theory are used to develop a potential energy surface that allows for the full three-dimensional motion of the incident atom and the reconstruction of the bonding carbon atom, which must pucker out of the surface to form a stable bond. Classical methods are used to compute trapping cross sections as a function of incident energy. The C-H bond, once formed, rapidly dissociates without a mechanism to dissipate its excess energy. However, a number of long-lived trapping resonances exist, and for impact parameters below 1 A or so, several percent of the incident H atoms can remain trapped for 1 ps or more. This long-time trapping probability increases significantly when additional lattice degrees of freedom are added to carry energy away from the C-H stretch. Trapping can also increase with an increasing collision impact parameter, as H vibrations parallel to the surface become excited, leaving less energy in the C-H stretch. The trapping cross section at 1 ps reaches a maximum of 0.2 A2 for an H atom energy of 0.3 eV. Assuming that any atoms remaining trapped after 1 ps fully relax and stick, we estimate a lower bound for the sticking probability of H and D to be 0.024 and 0.050, respectively, about an order of magnitude below the experimental values.