Notation

The HOOMD-blue documentation uses the following mathematical notation.

General notation:

$x$	Scalar.
$\vec{a}$	Vector.
$a$	Magnitude of the vector $\vec{a}$.
$\hat{a}$	Unit vector in the direction of $\vec{a}$.
$\mathbf{A}$	Matrix.
$\mathbf{b}$	Quaternion.
$\vert \mathbf{b} \vert$	Magnitude of a quaternion.
$i$, $j$, $k$	Indices.
$i$	$\sqrt{-1}$ in some contexts.
$\mathrm{function}$	A mathematical function.
a $[\mathrm{length}]^2$	The quantity “a” has dimensions of $\mathrm{length}^2$.

Symbol definitions:

$\vec{v}_{ij}$	$\vec{v}_j - \vec{v}_j$
$\vec{r}$	Position.
$\vec{v}$	Velocity.
$\mathbf{q}$	Orientation.
$m$	Mass.
$\vec{p}$	Momentum.
$I$	Moment of inertia.
$q$	Charge.
$N$	Number.
$L$	Length.
$V$	Volume.
$P$	Pressure.
$\rho$	Number density.
$\vec{a}_1$, $\vec{a}_2$, $\vec{a}_3$	Box unit cell vectors.
$\vec{F}$	Force.
$\vec{\tau}$	Torque.
$U$	Potential energy.
$K$	Kinetic energy.
$E$	Total energy.
$T$	Temperature.
$k$	Boltzmann’s constant in some contexts. Typically appears multiplying temperature: $kT$.
$k$	Spring constant in some contexts.
$\beta$	$\frac{1}{kT}$
$t$	Time.