Mixed Newtonian–Lagrangian Approach for the Analysis of Flexible Aircraft Dynamics

A method for deriving low-order models for flexible aircraft by means of a mixed Newtonian-Lagrangian approach is proposed. Lagrange equations are used for flexible degrees of freedom, discretized by means of the Galërkin method. The evolution of transport degrees of freedom (position and attitude variables) is obtained by means of Newton's second law and a generalized Euler equation. A strong link with conventional rigid aircraft equations of motion is maintained, which allows to highlight those terms less relevant for aircraft response. When negligible, these terms are removed, and a minimum-complexity flexible aircraft model is derived, suitable for realtime simulation and control law synthesis. Numerical results demonstrate how the approach correctly represents flexibility effects on aircraft response for a large transport aircraft model.