Documentation / @interstellar-tools/equations / rot3

Function: rot3()

function rot3(theta: Radians): Matrix3x3Type;

Defined in: helpers/rot-3.ts:38

Construct a right-handed rotation matrix about the z-axis (often written R₃).

This returns the 3×3 direction cosine matrix (DCM) for an active rotation by angle theta around the +Z axis:

$${\mathbf{R}}_3(\theta )=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0\\ \sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]$$

Notes:

• theta is in radians.
• Matrix layout is row-major: M[row][col].
• Common in 3-1-3 / 3-2-1 rotation sequences (e.g., IAU pole + prime meridian rotations) and general 3D coordinate transforms.

Parameters

Parameter	Type	Description
theta	Radians	Rotation angle ($\theta$) in radians (finite).

Returns

Matrix3x3Type

3×3 rotation matrix (${\mathbf{R}}_3(\theta )$) (row-major).

Throws

If theta is not a finite number.

Example

// Rotate about +Z by 90°:
const R = rot3(Math.PI / 2);