On-body propagation is one of the dominant propagation mechanisms in wireless body area networks (WBANs). It is characterized by near-field body-coupling and strong body-scattering effects. The temporal and spatial properties of on-body channels are jointly affected by the antenna polarization, the body posture, and the body motion. Analysis on the time variant properties of on-body channels relies on a good understanding of the dynamic body scattering, which is highly dependent on specific scenarios. In this paper, we develop an analytical model to provide a canonical description of on-body channels in both time and space domains to investigate the on-body propagation over the trunk surface of a walking human. The scattering from the arms and the trunk in different dimensions is considered with a simplified geometrical description of the body and of the body movements during the walk. A general full-wave solution of a polarized point source with multiple cylinder scattering is derived and extended by considering time evolution. The model is finally validated by deterministic and statistical comparisons to different measurements in anechoic environments.