Geometrically-nonlinear composite beam solutions are discussed as structural models for airframes with slender subcomponents. As this is intended for aircraft applications, the beam equations of motion are written with respect to a moving reference frame, which is rigidly-attached to a fixed point on the aircraft. Three different solution methods are then discussed, corresponding to a displacement-based formulation, a strain-based formulation, and a hybrid formulation in intrinsic variables. Key issues in numerical solution are discussed, including the parametrization of the finite rotations and linearization around arbitrary equilibrium conditions.