Terminology and Standards

The following terms, symbols, and decorators are used in text and diagrams throughout this guide.

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.

Acronym	Expansion
AOA	Angle Of Attack. Also named alpha.
AOS	Angle Of Sideslip. Also named beta.
FRD	Coordinate system where the X-axis is pointing towards the Front of the vehicle, the Y-axis is pointing Right and the Z-axis is pointing Down, completing the right-hand rule.
FW	Fixed-wing (planes).
MC	MultiCopter.
MPC	MultiCopter Position Controller or Model Predictive Control
NED	Coordinate system where the X-axis is pointing towards the true North, the Y-axis is pointing East and the Z-axis is pointing Down, completing the right-hand rule.
PID	Controller with Proportional, Integral and Derivative actions

Variable	Description
`x, y, z`	Translation along coordinate axis x, y, and z, respectively.
`r`	Position vector: `r = [x y z]^T`
`v`	Velocity vector: `v = r`
`a`	Acceleration vector: `a = v = r`
`α`	Angle of attack (AOA).
`b`	Wing span (from tip to tip).
`S`	Wing area.
`AR`	Aspect ratio: `AR = b^2 / S`
`β`	Angle of sideslip (AOS).
`c`	Wing chord length.
`δ`	Aerodynamic control surface angular deflection. A positive deflection generates a negative moment.
`φ, θ, ψ`	Euler angles: roll (=Bank), pitch, and yaw (=Heading).
`Ψ`	Attitude vector: `Ψ = [φ θ ψ]^T`
`X, Y, Z`	Forces along coordinate axis x, y, and z.

Subscripts / Indices	Description
a	Aileron.
e	Elevator.
r	Rudder.
Aero	Aerodynamic.
T	Thrust force.
w	Relative airspeed.
x, y, z	Component of vector along coordinate axis x, y and z.
N, E, D	Component of vector along global north, east and down direction.
l	Local-frame. Default for PX4 related variables.
b	Body-frame.
w	Wind-frame.