In the UCNτ 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 UCNτ magnetogravitational 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 UCNτ 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.