Function lupnt::RotSideralMotionDot

Function Documentation

Mat3 lupnt::RotSideralMotionDot(Real t_tdb)

Returns the exact time derivative dR_s/dt of the sidereal-motion rotation matrix (see RotSideralMotion) at epoch t_tdb, evaluated using the Earth rotation rate w_E (from the EOP length-of-day, or the analytic derivative of the SPICE-fitted UT1-UTC if InitFrameConversionFromSpice has fitted a model covering t_tdb).

If InitFrameConversionFromSpice has fitted a SPICE-derived EOP model (see ComputeEopFromSpice) covering t_tdb, the fitted UT1-UTC (and its exact analytic time derivative) is used to compute theta_era and the Earth rotation rate w_E — consistently with RotSideralMotion — in place of the loaded IERS EOP table’s UT1-UTC/LOD.

Used internally by GcrfToItrf/ItrfToGcrf to compute the velocity-transformation term R_GcrfToItrf_dot = R_po * R_s_dot * R_pn, which accounts for the Earth-fixed frame’s rotation rate when converting velocities between GCRF and ITRF.

Note

Astrodynamics Convention & Modeling Reference, Version 1.1, Page 36

Parameters:

t_tdb – Epoch [s, TDB since J2000]

Returns:

3x3 matrix dR_s/dt [1/s] (time derivative of the sidereal-motion rotation matrix)