I’m working on several things, and it’s possible I’ll have a technical post ready later today. OTOH, I’m going to a dinner party tonight, so this will be a short schoolday.
As you might guess from the recent posts about rotations, I have gotten caught up in rotating coordinate systems. The original cause was a nifty equation in the airplane control books. As is true of too many things, I can even find that equation in an old schoolbook, in this case my ancient copy of Goldstein. Worse, I highlighted it all those years ago. That equation writes the rotation axis in terms of the derivatives of the Euler angles and their rotation axes.
Right now, however, I am playing with two more familiar and elementary equations. Well, you would have seen them in upper-division classical mechanics; before that, you usually just get them in fragments (radial and tangential components). Eventually they are usually written something like
(If you recognize them at all, you may know the term as the Coriolis effect.) I have a derivation of them that gives me some insight into exactly what’s what. It’s at what I call stage 2: the math is all written out, but I need to add the surrounding discussion.
Playing with these equations has sometimes interfered with my making regular progress in the study of surfaces (Bloch). Oh, I still need to address an old comment about gluing schemes….
A friend has picked up the Cox-Little-O’Shea book on algebraic geometry, so I’m working thru that with him.
And, of course, there’s principal components / factor analysis. I’ve done most of the remaining work for Malinowski, but I need to add a lot of commentary, too. And I have one sort-of-open question about something he did.