Formulation of the Flight Dynamics of Flexible Aircraft Using General Body Axes

An inertially-coupled formulation for the flight dynamics of flexible aircraft undergoing small deformations is developed. The availability of a structural-dynamic finite element model of the aircraft is presupposed. With all the coupled dynamics taken into account, an arbitrary choice of the body reference frame can be made. This frame is also allowed to be noncoincident with the frame of reference used to calculate the aerodynamic loads. In the equations of motion, the inertial coupling terms are linearized in the elastic displacements around a calculated equilibrium condition. Appropriate modes of vibration are then used in the calculation of the dynamic deformation of the structure. A simple quasi-steady incremental aerodynamic model based on the vortex-lattice method is used. The formulation is tested in the flight simulation of an idealized forward-swept-wing aircraft model. Numerical results show that, under small deformations, different body axes lead to the same overall motion of the aircraft with respect to an inertial frame. The stiffness level at which geometrically nonlinear formulations would become necessary is also determined.