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.