# 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.