Should coordinate transformations from J2000 to ITRF93 in quaternions be cyclic?

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'
)


See the picture for how the first quaternion element undergoes periodic change over time: