I used SPICE's pxform at an interval of epochs to determine the transformation from J2000 (inertial) to ITRF93 (Earth body-fixed) frame. Then, I converted these rotation matrices to quaternions with SPICE's m2q function. Lastly, I converted it to the alternative quaternion formulation where the real part is the last element.
I am looking at the result and I'm not sure that it's reasonable since there are a lot of cyclic fluctuations in the quaternion values. Previously, I have done transformations for J2000 to MOON_ME (moon body-fixed) frame and there was not these cycles in the same epoch interval. Is my result reasonable or do I need to rethink how I'm using SPICE for this to make sense?
The kernels I'm using are as follows:
KERNELS_TO_LOAD=( 'KernelsMoon\PCK\pck00010.tpc', 'KernelsMoon\PCK\moon_pa_de421_1900-2050.bpc', 'KernelsMoon\PCK\earth_000101_200729_200507.bpc' 'KernelsMoon\FK\moon_080317.tf' 'KernelsMoon\SPK\de430.bsp' 'KernelsMoon\LSK\naif0012.tls.pc' )