  In the UCN{\tau} experiment, ultracold neutrons (UCN) are confined by
magnetic fields and the Earth's gravitational field. Field-trapping mitigates
the problem of UCN loss on material surfaces, which caused the largest
correction in prior neutron experiments using material bottles. However, the
neutron dynamics in field traps differ qualitatively from those in material
bottles. In the latter case, neutrons bounce off material surfaces with
significant diffusivity and the population quickly reaches a static spatial
distribution with a density gradient induced by the gravitational potential. In
contrast, the field-confined UCN -- whose dynamics can be described by
Hamiltonian mechanics -- do not exhibit the stochastic behaviors typical of an
ideal gas model as observed in material bottles. In this report, we will
describe our efforts to simulate UCN trapping in the UCN{\tau}
magneto-gravitational trap. We compare the simulation output to the
experimental results to determine the parameters of the neutron detector and
the input neutron distribution. The tuned model is then used to understand the
phase space evolution of neutrons observed in the UCN{\tau} experiment. We will
discuss the implications of chaotic dynamics on controlling the systematic
effects, such as spectral cleaning and microphonic heating, for a successful
UCN lifetime experiment to reach a 0.01% level of precision.
