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I used Cassini's Laws to derive an approximate solution to the Moon's rotation axis. The error is on the order of 5 arcminutes. I still need to correct for physical libration. I also need to find test data for the Moon's prime meridian so that I can implement the spin angle calculation. (I could use test data for all the planets' spins, for that matter.)
Acknowledgements
Moon libration data for the years 2020-2022 comes from NASA's Scientific Visualization Studio.
mooninfo_2020.txt comes from: Moon Phase and Libration 2020
mooninfo_2021.txt comes from: Moon Phase and Libration 2021
mooninfo_2022.txt comes from: Moon Phase and Libration 2022
These Moon Phase and Libration pages contain some wonderful videos, images, and explanatory text that help make the complexities of the Moon's orbit and libration understandable.
Further Reading
The PDF document Computation of the Quantities Describing the Lunar Librations in The Astronomical Almanac provides a detailed explanation of the meaning of lunar libration quantities like sub-solar angles, sub-earth angles, and polar position angles.