Had a quick look at "Nutation" on the Wiki link.
It puts me in mind of spinning coins on a table, bottles with some fluid contents wobbling on their circular base, gyroscopes etc.
If the Earth has nutation as you describe and an extra gravitational influence was introduced, such as a close encounter with a large comet, it is imagineable that it might cause a 180 degree flip of the Earth's rotational axis. Yes??
That would add weight at least, if not confirm, Immanuel Velikovsky's theory he put forward some 60 years ago, that far from "Darwin's Theory of Evolution" (still a theory) proposing that life on Earth is a result of gradual changes of environment over millions of years, that it is the result of relatively recent catastrophic events such as the near collision of Venus (then a comet) with Earth at the time of Moses, and that it was Venus not Moses who parted the Red Sea and caused the pestilence and 40 years of darkness. Also that mutation of species is caused by exposure to strong electromagnetic forces.
I think the French proved that at Mururoa Atoll.
Darwin's Theory is popular because it is promoted by the elites who control the education systems and who believe in the concept of greater and lesser species of humans.
The elites are the most degenerate people on Earth. One only has to look at the behavior of the royals, politicians and hollywoodstars to realise that.
Read more about Velikovsky here:-
en.wikipedia.org/wiki/Immanuel_Velikovsky