I have been perplexed for a while by the use of the term "nutating" in espresso preparation. Nutation is defined in various ways here
or even here.
It used to apparently be a fancy way of describing the nodding of the head.
In botany, it refers to the slight bend a plant may make as it grows.
In astronomy, it is the wobble in the oscillation of the precession of the axis of a rotating body.
None of these terms fully capture the idea of the motion I think we all assume we understand in our colloquial use is such phrases as "nutating tamp," but perhaps one of the reasons we do not get consistent results is because we are all doing our "nutating" tamp a bit differently.
In truth, to really be a true nutating motion when we tamp, we would have to wobble the tamper from side to side a bit while rotating. Okay, yes, that DOES probably happen, but not by intention, I don't think. Unless, I am wrong, most people are simply spinning or rotating the tamper while applying pressure. The major variables here are the amount of pressure applied and the amount of spinning/rotating done.
My personal experience is that any form of true nutation (i.e., wobble) is undesirable are it makes the puck uneven. I have also found that excessive pressure with the relatively asymmetric and dynamically changing forces of rotation can lead to channeling. So, what I tend to do is more akin to light polishing. Essentially I use only the weight of the tamper for my final "nutating" step and I simply rotate the tamper. This reveals any asymmetry because if the puck is not level, the tamper will wobble a bit as it rotates, which I suppose is actually the nutation.
So in fact I am really doing an anti-nutating step, I guess.
Anyway, I would be very interested to hear other people's thoughts about this topic, what they do, what their experience has been, and what the thoughts are on standardizing what is meant by nutating, which may not be nutation at all.