A general body axis system, denoted by Xb, Yb, and Zb, is chosen for a rotating coordinate system relative to the rocket. Xb is anchored to the longitudinal axis of the rocket through the flight. The angles that can be defined by transforming between the Earth-surface system and the body system can be denoted using the standard roll, pitch, and yaw (φ, θ, ѱ) Euler Angles that aircraft often use.
For an inertial system, an Earth-surface frame is chosen denoted by Xe, Ye, and Ze. This system’s origin is at the rocket’s center of gravity (CG).
TRANSLATIONAL EQUATIONS OF MOTION
ROTATIONAL EQUATIONS OF MOTION
P, Q, and R are roll, pitch, and yaw rates
L, M, and N are rolling, pitching, and yawing moments
u,v, and w are components of the vehicle’s velocity