Documentation / @interstellar-tools/equations / rot1

Function: rot1()

function rot1(theta: Radians): Matrix3x3Type;

Defined in: helpers/rot-1.ts:38

Construct a right-handed rotation matrix about the x-axis (often written R₁).

This returns the 3×3 direction cosine matrix (DCM) for an active rotation by angle theta around the +X axis, using the common aerospace convention:

$${\mathbf{R}}_1(\theta )=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \theta & -\sin \theta \\ 0& \sin \theta & \cos \theta \end{array}\right]$$

Notes:

• theta is in radians.
• Matrix layout is row-major: M[row][col].
• Useful for composing 3-1-3 / 3-2-1 sequences (e.g., IAU body orientation) and for general 3D frame transforms in mapping pipelines.

Parameters

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

Returns

Matrix3x3Type

3×3 rotation matrix (${\mathbf{R}}_1(\theta )$) (row-major).

Throws

If theta is not a finite number.

Example

// Rotate a vector about +X by 90°:
const R = rot1(Math.PI / 2);