Modeling aircraft and spacecraft are simplest if you use a coordinate system fixed in the body itself. In the case of aircraft, the forward direction is modified by the presence of wind, and the craft's motion through the air is not the same as its motion relative to the ground.
The noninertial body coordinate system is fixed in both origin and orientation to the moving craft. The craft is assumed to be rigid.
The orientation of the body coordinate axes is fixed in the shape of body.
The x
-axis points through
the nose of the craft.
The y
-axis points to the
right of the x
-axis (facing in the pilot's
direction of view), perpendicular to the x
-axis.
The z
-axis points down
through the bottom of the craft, perpendicular to the x
-y
plane
and satisfying the RH rule.
Translations are defined by moving along these axes by distances x
, y
,
and z
from the origin.
Rotations are defined by the Euler angles P
, Q
, R
or
Φ, Θ, Ψ. They are
P
or Φ: Roll about
the x
-axis
Q
or Θ: Pitch about
the y
-axis
R
or Ψ: Yaw about
the z
-axis
Unless otherwise specified, by default the software uses ZYX rotation order for Euler angles.
The noninertial wind coordinate system has its origin fixed in the rigid aircraft. The coordinate system orientation is defined relative to the craft's velocity V.
The orientation of the wind coordinate axes is fixed by the velocity V.
The x
-axis points in the
direction of V.
The y
-axis points to the
right of the x
-axis (facing in the direction
of V), perpendicular to the x
-axis.
The z
-axis points perpendicular
to the x
-y
plane
in whatever way needed to satisfy the RH rule with respect to the x
-
and y
-axes.
Translations are defined by moving along these axes by distances x
, y
,
and z
from the origin.
Rotations are defined by the Euler angles Φ, γ, χ. They are
Φ: Bank angle about the x
-axis
γ: Flight path about the y
-axis
χ: Heading angle about the z
-axis
Unless otherwise specified, by default the software uses ZYX rotation order for Euler angles.