Introduction Airplane Equations of Motion (EOM) Coordinate Systems Static Transitions Dynamic Tra
AERO 480 and MECH 6091-Flight
Control Systems Lecture 2- Equations of
Motion - Reference Frames (Prof. Youmin Zhang)
Prof. Youmin Zhang
September 14, 2023
,Outline Airplane Equations of Motion - Goal to be Achieved by the Course Airplane Configurations Coordi
Contents to be Covered
Basic definitions and concepts, aircraft configurations
Forces and moments acting on aircraft, coordinate systems
Aircraft equations of motion, longitudinal and lateral-
directional equations of motion (see next slides for an
overall view - one of main goals to achieve after the course)
Linearization of equations of motion, state-space form,
stability derivatives
Trim, static stability (longitudinal and lateral-directional)
Dynamic stability (longitudinal motion)
Dynamic stability (lateral-directional motion, to be covered
as time permitted)
Brief introduction to flight control system design via classic
and modern control theory (to be covered as time
permitted)
Brief introduction to fault-tolerant flight control systems
(optional)
,Introduction Airplane Equations of Motion (EOM) Coordinate Systems Static Transitions Dynamic Tra
Introduction
In order to be able to derive Equations Of Motion (EOM) foran
airplane, one needs to know
Coordinate systems
Static transition between coordinate systems
Kinematic and Kinetics
Dynamic transition between coordinate systems
We will cover following subjects in this lecture
Body, Stability and Wind Coordinate Systems
Static Transition
Dynamic Transition
Nonlinear Equations of Motion of an Airplane
We use abbreviation CS for Coordinate Systems in this lecture.A
very useful webpage:
http://people.rit.edu/pnveme/EMEM682n/index.html
, Introduction Airplane Equations of Motion (EOM) Coordinate Systems Static Transitions Dynamic Tra
Summary: Airplane Equations of Motion (EOM)
Translational Equations of Motion:
m(u˙ + qw − rv) = X
m(v˙ + ru − pw) = Y
m(w˙ + pv − qu) = Z
Rotational Equations of Motion
Ixx ṗ − Ixz ṙ + qr(Izz − Iyy ) − Ixz pq = L
Iyy q̇ + rp(Ixx − Izz ) − Ixz (p2 − r 2 ) = M
−Ixzp˙ + Izzr˙ + pq(Iyy − Ixx) − Ixzqr = N
Rotational Kinematic:
p = φ˙ − sin θψ˙
q = cos φθ˙ + sin φ cos θψ˙
r = cos φ cos θψ˙ − sin φθ˙
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