Equations of Motion of an Aircraft

Abstract

In this chapter, we apply the results derived in Chap. 1, to deduce the equations of motion of an aircraft. Specifically, we discuss a choice of the aircraft state vector and body reference frame, which are suitable for the study of the stability properties of aircraft. An entire section is dedicated to the analysis of the functional dependencies of the forces and the moment of the forces acting on an airplane so that the equations of motion can be simplified without losing meaningfulness. After having provided the equations of motion of an aircraft in terms of the Tait-Byran angles and the Euler parameters, we linearize these equations. Since the aircraft dynamics is captured by a set of implicit nonlinear differential equations, the details of this linearization process are discussed at length. Lastly, we decouple the linearized equations of motion of an aircraft, we apply the modal decomposition technique to analyze the short period and phugoid modes characterizing the longitudinal dynamics, and we discuss the roll, the spiral, and Dutch roll modes characterizing the lateral-directional dynamics.