During the week I came across a link to a sequence of three old movies about the Lagrangian and Eulerian viewpoints in fluid mechanics. Here’s a direct YouTube link to the first:
and, just in case you’re interested, here’s the link I found first, which is on a fluid mechanic’s blog. (Those of us who have seen “Forbidden Planet” know that a man can be “the best quantum mechanic in the system”… I see no reason not to call someone a fluid mechanic.)
And speaking of fluid mechanics…
Someone reminded me of Terry Tao’s blog.
(He’s a Fields Medalist I’ve spoken of before because of his interest in education.)
He has a derivation of the tsunami wave equation – that is, of the equation we use for tsunamis until they get close to shore.
He also has, on the left-hand side of his blog under “articles by others”, several things which might be of interest. I’ve only looked at five of them so far. Here are direct links to two of them.
William Thurston On proof and progress in mathematics was very interesting. I spoke of him before, too. This article was written before he completed his book on 3-D geometry – but it explains why he set out to write it.
Po Bronson How not to talk to your kids is a startling article demonstrating that children who are praised for hard work do better than children who are praised for being intelligent.
It’s been another productive but relatively uneventful week: I’ve seen several interesting things, and I’ve finished off three small problems; but I haven’t done anything major.
In particular, I decided to let the subject of multicollinearity lie fallow for a while – I want to pick it up again with somewhat fresher eyes. No, I’m not done with it by a long shot.
Two of the problems I worked out are for time on an elliptical orbit… one asks for position given time, and the other asks for time given position. Getting the time is the easy one: work out an angle, compute its sine, stir in the eccentricity, and get an answer directly.
Getting the position is harder… but it’s the one we need to solve – repeatedly – in order to make an animation. It requires numerical methods, and can be very inaccurate near periapse for nearly parabolic orbits.
On the other hand, Mathematica makes short work of the examples… it’s just a matter of being careful, as usual.
In addition, the examples illustrate the use of canonical units, again.
The third problem I solved was for a simple beam with a single concentrated force – but the point was to get Mathematica to solve it using a Dirac delta function. It’s nice.
… OK, I’m going out to lunch with a friend, and I’ll post this when I return….