Bold face variables indicate vectors or matrices and non-bold face variables represent scalars.
The default frame for each variable is the local frame: .
Right superscripts represent the coordinate frame.
If no right superscript is present, then the default frame is assumed.
An exception is given by Rotation Matrices, where the lower right subscripts indicates the current frame and the right superscripts the target frame.
Variables and subscripts can share the same letter, but they always have different meaning.
Translation along coordinate axis x,y and z respectively.
Angle of attack (AOA).
Wing span (from tip to tip).
Angle of sideslip (AOS).
Wing chord length.
Aerodynamic control surface angular deflection. A positive deflection generates a negative moment.
Euler angles roll (=Bank), pitch and yaw (=Heading).
Forces along coordinate axis x,y and z.
Moments around coordinate axis x,y and z.
Mach number. Can be neglected for scale aircraft.
Vector part of Quaternion.
Hamiltonian attitude quaternion (see 1 below)
Rotation matrix. Rotates a vector from frame to frame .
Leading-edge sweep angle.
Angular rates around body axis x,y and z.
Angular rate vector in body frame:
General state vector.
1 Hamiltonian attitude quaternion. . describes the attitude relative to the local frame . To represent a vector in local frame given a vector in body frame, the following operation can be used: (or instead of if is not unitary). represents a quaternionized vector: