The residuals in the phase values show a really cool Moire pattern.
Right.
That answers the question posed at the start of this thread.
Are the residuals random noise? Nope. There's almost nothing
random about them.
Students may find this easier to understand if you show them
a Moiré pattern produced by the model on the basis of no data
whatsoever. It arises simply because the rotation period is
incommensurate with the sampling interval.
which plots the residuals as a function of angular *velocity*
so you can see that when the rotation rate (in degrees) is
at or near an integer multiple of the sampling rate, the pattern
is single-valued. When it is at or near an odd half-integer
multiple of the sampling rate, the pattern is two-valued.
And so on. This leaves no doubt that we have identified
correctly the fundamental physics (aka math) issues involved.
(These patterns are related to the "aliasing" phenomenon
that you see in Fourier transforms when the sampling
interval is incommensurate with the underlying physics,
but that's probably more than the students want to know
at this point.)
We need to come up with a better name for these "residuals".
They were residuals with respect to an ultra-simple model,
but our fancier model can predict them more-or-less exactly,
so they're not residuals with respect to the fancy model.