Mean-axis models of flight dynamics for flexible aircraft are being utilized more frequently in dynamics and controls research. The mean-axis equations of motion are traditionally developed with Lagrangian mechanics and are typically simplified using assumptions regarding the effects of elastic deformation. Although widely accepted in literature, the formulation and assumptions may be confusing to a user outside of the flight dynamics field. In this thesis, the equations of motion are derived from first principles utilizing Newtonian mechanics. Using this framework, the formulation offers new insight into the equations of motion and explanations for the assumptions. A three-lumped-mass idealization of a rolling flexible aircraft is presented as an example of the mean-axis equations of motion. The example is used to investigate the effects of common simplifying assumptions. The equations of motion are developed without any such assumptions, and simulation results allow for a comparison of the exact and simplified dynamics.