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

A novel method for deriving simplified models of flexible aircraft dynamics by means of a mixed Newtonian–Lagrangian approach is proposed. Lagrange equations are used for deriving the dynamic model for flexible degrees of freedom, discretized by means of a standard Gal ̈erkin method, while the evolution of transport degrees of freedom (translation and attitude variable) is obtained by means of second Newton’s Law and generalized Euler equations, suitable for describing the dynamics of deformable bodies. The method allows for easily highlighting those terms less important in the dynamic response of the aircraft, thus making it possible to simplify the model as much as possible, keeping its complexity down to a minimum level. This feature is particularly interesting when the dynamic model is used for the derivation of control laws and flexibility effects need to be accounted for only if coupling with manoeuvre and/or closed loop control tasks is relevant. Numerical simulation demonstrates the viability of the modeling approach, showing that flexibility effects are correctly represented.