In this dissertation, we investigate the radiation belts as a dynamic system, paying particular attention to adiabatic motion and the related adiabatic invariant coordinate system. The theoretical foundations, based on classical mechanics and single particle plasma physics, are reviewed to provide a framework for the dissertation. With this foundation, we develop numerical methods to implement the calculation of adiabatic invariants from magnetic field models, being the first to do so in the literature with a concentrated focus on (a) rigorously documenting each computational step, (b) addressing significant sources of uncertainty, and (c) justifying selections of algorithm parameters. We apply these methods to quantifying the global adiabatic motion patterns of electrons in the outer radiation belt through a new computational method called invariant matching. These global adiabatic motion patterns are visualized as vector plots showing the displacement of mirror points throughout the magnetosphere. The plots display established features of radiation belt dynamics, such as the Dst effect, drift orbit bifurcation, and drift shell splitting. Finally, we combine four magnetic field models (two empirical and two magnetohydrodynamic) with observational satellite data from the Van Allen Probes. A study is designed to bolster existing results around the significant open question of what causes outer radiation belt electrons to accelerate to relativistic levels. Modern and highly cited results from the literature are reevaluated using the dissertation’s rigorous tooling and, for the first time, multiple magnetic field models. By using multiple magnetic field models, this dissertation demonstrates that the results are generally model-independent, which strengthens the conclusion that acceleration is primarily (but not always) driven by whistler-mode chorus waves. This dissertation is tied together by the theory of dynamical systems, the development of rigorous numerical methodology, and the purpose of describing the causal dynamics of electron acceleration in the outer radiation belts.