Derivation and Analysis of Rigid Aircraft Equations of Motion with Application to Longitudinal Dynamics

Abstract

Rigid body equations of motion of an aircraft involves kinetic and kinematic analysis of the vehicle. Pure motion of rigid bodies are translation and rotation hence, derivation of equation of motion of rigid aircraft in translation and rotation is the focus of this paper. Non-linearity and unsteadiness are common characteristics of a typical aerospace vehicles judging from control theory perspective Derivation of these equations with its dynamic parameters are stated as follows: Equation of translational motion ∑\(\Delta\)Fx=m(℧ ̇+ ZQ-℧R) ∑\(\Delta\)Fy=m(∀ ̇+ ℧R-Z℘) ∑\(\Delta\)Fz=m(Z ̇+ ℘∀-℧Q) Equation of rotation motion ∑\(\Delta\)L℘ ̇Ix -R ̇Jxz + QR (Iz-Iy) - ℘QJxz ∑\(\Delta\)M=Q ̇Iy +℘R(Ix-Iz) +(℘2-R2 ) jxz ∑\(\Delta\)N=R ̇Iz -℘ ̇Jxz + ℘Q (Iy-Ix) + QRJxz The derivation are carried out in body-fixed coordinate system with reference to Earth - fixed reference frame. The equations can be linearised at the neighbourhood of trimmed operating point (nominal trajectory) to obtain a simplified algebraic equations, written in form of transfer function of input and output for trajectory design, stability analysis and control system synthesis as extracted from: (postgraduate lecture’s notes of Internationals Institutes for Advance Aerospace Technologies of SUAI., St. Petersburg, Russia, 2009). Linearization process and decomposition to simple polynomials in frequency domain using Laplace transform tools is the subject of another paper.