# 术语 ​

## 符号 ​

• Bold face variables indicate vectors or matrices and non-bold face variables represent scalars.
• The default frame for each variable is the local frame: $\ell$. Right superscripts represent the coordinate frame. If no right superscript is present, then the default frame $\ell$ 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.

## Acronyms ​

AcronymExpansion
AOAAngle Of Attack. Also named alpha.
AOSAngle Of Sideslip. Also named beta.
FRDCoordinate 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.
FWFixed-wing (planes).
MCMultiCopter.
MPC 或 MCPCMultiCopter Position Controller. MultiCopter Position Controller. MPC is also used for Model Predictive Control.
NEDCoordinate 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.
PIDController with Proportional, Integral and Derivative actions.

## Symbols ​

Variable描述
$x,y,z$Translation along coordinate axis x,y and z respectively.
$\mathbf{r}$Position vector: $\mathbf{r}=\left[x\phantom{\rule{1em}{0ex}}y\phantom{\rule{1em}{0ex}}z{\right]}^{T}$
$\mathbf{v}$Velocity vector: $\mathbf{v}=\stackrel{\mathbf{˙}}{\mathbf{r}}$
$\mathbf{a}$Acceleration vector: $\mathbf{a}=\stackrel{\mathbf{˙}}{\mathbf{v}}=\stackrel{\mathbf{¨}}{\mathbf{r}}$
$\alpha$Angle of attack (AOA).
$b$Wing span (from tip to tip).
$S$Wing area.
$AR$Aspect ratio: $AR={b}^{2}/S$
$\beta$Angle of sideslip (AOS).
$c$Wing chord length.
$\delta$Aerodynamic control surface angular deflection. A positive deflection generates a negative moment. A positive deflection generates a negative moment.
$\varphi ,\theta ,\psi$Euler angles roll (=Bank), pitch and yaw (=Heading).
$\mathrm{\Psi }$Attitude vector: $\mathrm{\Psi }=\left[\varphi \phantom{\rule{1em}{0ex}}\theta \phantom{\rule{1em}{0ex}}\psi {\right]}^{T}$
$X,Y,Z$Forces along coordinate axis x,y and z.
$\mathbf{F}$Force vector: $\mathbf{F}=\left[X\phantom{\rule{1em}{0ex}}Y\phantom{\rule{1em}{0ex}}Z{\right]}^{T}$
$D$Drag force.
$C$Cross-wind force.
$L$Lift force.
$g$Gravity.
$l,m,n$Moments around coordinate axis x,y and z.
$\mathbf{M}$Moment vector $\mathbf{M}=\left[l\phantom{\rule{1em}{0ex}}m\phantom{\rule{1em}{0ex}}n{\right]}^{T}$
$M$Mach number. Can be neglected for scale aircraft.
$\mathbf{q}$Vector part of Quaternion.
$\stackrel{\mathbf{~}}{\mathbf{q}}$Hamiltonian attitude quaternion (see 1 below)
${\mathbf{R}}_{\ell }^{b}$Rotation matrix. Rotates a vector from frame $\ell$ to frame $b$. ${\mathbf{v}}^{b}={\mathbf{R}}_{\ell }^{b}{\mathbf{v}}^{\ell }$
$\mathrm{\Lambda }$Leading-edge sweep angle.
$\lambda$Aspect ratio. $$AR = b^2/S$$.
$w$Wind velocity.
$p,q,r$Angular rates around body axis x,y and z.
${\mathbit{\omega }}^{b}$Attitude vector. $$\Psi = [\phi \quad \theta \quad \psi]^T$$.
$\mathbf{x}$General state vector.
• 1 Hamiltonian attitude quaternion. Hamiltonian attitude quaternion. $$\boldsymbol{\mathrm{\tilde{q}}} = (q_0, q_1, q_2, q_3) = (q_0, \boldsymbol{\mathrm{q}})$$. To represent a vector in local frame given a vector in body frame, the following operation can be used: ${\stackrel{\mathbf{~}}{\mathbf{v}}}^{\ell }=\stackrel{\mathbf{~}}{\mathbf{q}}\phantom{\rule{0.167em}{0ex}}{\stackrel{\mathbf{~}}{\mathbf{v}}}^{b}\phantom{\rule{0.167em}{0ex}}{\stackrel{\mathbf{~}}{\mathbf{q}}}^{\ast }$ (or ${\stackrel{\mathbf{~}}{\mathbf{q}}}^{-1}$ instead of ${\stackrel{\mathbf{~}}{\mathbf{q}}}^{\ast }$ if $\stackrel{\mathbf{~}}{\mathbf{q}}$ is not unitary). $\stackrel{\mathbf{~}}{\mathbf{v}}$ represents a quaternionized vector: $\stackrel{\mathbf{~}}{\mathbf{v}}=\left(0,\mathbf{v}\right)$

### Subscripts / Indices ​

Subscripts / Indices描述
$a$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.

### Superscripts / Indices ​

Superscripts / Indices描述
$\ell$Local-frame. Local-frame. Default for PX4 related variables.
$b$Body-frame.
$w$Wind-frame.

## Decorators ​

Decorator描述
$\left({\right)}^{\ast }$Complex conjugate.
$\stackrel{˙}{\left(\right)}$Time derivative.
$\stackrel{^}{\left(\right)}$Estimate.
$\overline{\left(\right)}$Mean.
$\left({\right)}^{-1}$Matrix inverse.
$\left({\right)}^{T}$Matrix transpose.
$\stackrel{~}{\left(\right)}$Quaternion.