Documentation / @interstellar-tools/equations / bodyFixedFromInertialDcmIAU

Function: bodyFixedFromInertialDcmIAU()

function bodyFixedFromInertialDcmIAU(
  alphaP: Radians,
  deltaP: Radians,
  W: Radians
): Matrix3x3Type;

Defined in: cartography/body-fixed-from-inertial-dcm-iau.ts:54

Build the IAU-style inertial → body-fixed direction cosine matrix (DCM).

This constructs the 3×3 rotation matrix that transforms a vector expressed in an inertial frame (commonly ICRF/J2000-like) into the body-fixed, planetocentric frame defined by:

• the body's north pole right ascension (${\alpha }_p$),
• the body's north pole declination (${\delta }_p$),
• the prime meridian angle ($W(t)$).

Using the common 3-1-3 sequence:

$${\mathbf{R}}_{\text{BF}\leftarrow \text{ICRF}}={\mathbf{R}}_3(W){\mathbf{R}}_1(\frac{\pi }{2}-{\delta }_p){\mathbf{R}}_3(\frac{\pi }{2}+{\alpha }_p)$$

Notes:

• All angles are in radians.
• Matrices are row-major (M[row][col]).
• The returned matrix can be applied to inertial vectors via applyMatrix3(R, v).

Parameters

Parameter	Type	Description
alphaP	Radians	Right ascension of the north pole (${\alpha }_p$) in radians (finite).
deltaP	Radians	Declination of the north pole (${\delta }_p$) in radians (finite).
W	Radians	Prime meridian angle ($W(t)$) in radians (finite).

Returns

Matrix3x3Type

3×3 DCM (${\mathbf{R}}_{\text{BF}\leftarrow \text{ICRF}}$) (row-major).

Throws

If any input is not a finite number.

Example

// Given IAU pole and prime meridian angles (radians):
const R = bodyFixedFromInertialDcmIAU(alphaP, deltaP, W);

// Transform an inertial vector into body-fixed:
const vBF = applyMatrix3(R, vICRF);

See

• applyMatrix3
• https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/pck.html NAIF SPICE PCK Required Reading (RA, DEC, W orientation model)
• https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html NAIF SPICE Frames Required Reading (reference frames and transformations)
• https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/cspice/tipbod_c.html SPICE tipbod_c (inertial → body-equator-and-prime-meridian rotation)
• https://www.iau.org/WG100/WG100/Home.aspx IAU WGCCRE / WG100 (cartographic coordinates & rotational elements reports)
• https://aa.usno.navy.mil/downloads/reports/Archinaletal2011a.pdf Archinal et al. (2011) IAU WGCCRE report (pole and prime meridian definitions)