ABSTRACT
According to Newton’s 2nd Law, the equations of motion written in the local aircraft frame for a rigid body, are given by: F mdV V/ .dt m+ ω Similarly, the angular equation is expressed by: M dh dt h/ ω . Where F is the force applied, M is the moment, V is the velocity vector, and h is the angular moment. It is possible to write h as a product between the inertia tensor and the angular velocity: [ ]I ω . Where ω is the angular velocity and [I] is the inertia tensor. Or, using the vector components and neglecting terms usually small in the matrix:
x m dt qw rv y m dt ru pw z m dt pv qu
+= − += − += −
[ /du ] [ /dv ] [ /dw ]
and
L I dt I dr d qr M I dt p
+
−
( /dp ) (− / )t pq ( )I I− ( /dq ) (I+ 2 r I I
N I dt qr dp d pq xx zz
2 ) (p ) ( /d ) (I / )t ( )I I .
