I forgot to include an option about this in the previous Dorky Poll, but this is one of the best ways I know to sort out righteous physicists from heathen mathematicians:
Choose wisely.
I forgot to include an option about this in the previous Dorky Poll, but this is one of the best ways I know to sort out righteous physicists from heathen mathematicians:
Choose wisely.
What, no lambda is the latitude option?
Burn the infidel azimuthal thetas!
i prefer euler angles. not.
I worked with deep space stations with three mounts — ha-dec (‘polar’), az-el, and x-y — and had to translate between them.
Quaternions are used in GN&C (Guidance Navigation and Control) of spacecraft and some aircraft for 3-D rotations of spacecraft attitudes. This uses less space and time in old fashioned computers than Euler angles or other representations. I wrote software at NASA/JPL for the Galileo Jupiter orbiter.
That is, the Galileo itself used quaternions in the flight software, so my simulations used quaternions for Validation and Verification (V&V) of command sequences before uplinking them to the spacecraft. I used matrices and angles to avoid making any of the same mistakes that the flight software might have. So I alone interconverted the two representations.
But one older guy at JPL who had not even a college degree could do calculations with quaternions in his head. He could
look at my scores of pages of matrix equations and say: “Yup. That’s right.”
The complication was that the Galileo was a dual-spinner spacecraft, which had never before been used interplanetary.
One part (rotor) could be fixed to the other (stator), or rotate at fixed speed, or by command, or be inertial. The articulated scan platform with telescopes of various frequencies was hinged to the rotor.
So when you moved the platform to scan, say, the Great Red Spot, the whole system wobbled and nutated in absurdly complicated ways, which I had to simulate to ensure that nothing drastic happened (point telesope at sun and burn it out, throw spacecraft into chaotic oscillation).
Galileo worked.
There are several papers on quaternionic General Relativity. There’s no a priori reason to believe that, say, Mass must be a real number, and not quaternions o0r something stranger.
That thread we had about imaginary numbers — are they imaginary, or just as real as the reals? That goes for quaternions, too.
But you have to use them correctly…
My vote is for the second choice, but only because it’s the closest. With planar features strike (azimuthal angle) is usually theta, dip (polar angle) is usually delta; linear features are described by plunge (polar angle), “p”, and trend (azimuth), beta.
I had to pull out a text book to find this since the symbols are hardly used, unless you have to write out the formulas for calculating things like apparent dip or the trend and plunge of the line created by two intersecting planes – both of which can be found on a stereonet much faster.
You've read the blog, now try the books:
How to Teach Relativity to Your Dog is published by Basic Books. "“Unlike quantum physics, which remains bizarre even to experts, much of relativity makes sense. Thus, Einstein’s special relativity merely states that the laws of physics and the speed of light are identical for all observers in smooth motion. This sounds trivial but leads to weird if delightfully comprehensible phenomena, provided someone like Orzel delivers a clear explanation of why.” --Kirkus Reviews "Bravo to both man and dog." The New York Times.
How to Teach Physics to Your Dog is published by Scribner. "It's hard to imagine a better way for the mathematically and scientifically challenged, in particular, to grasp basic quantum physics." -- Booklist "Chad Orzel's How to Teach Physics to Your Dog is an absolutely delightful book on many axes: first, its subject matter, quantum physics, is arguably the most mind-bending scientific subject we have; second, the device of the book -- a quantum physicist, Orzel, explains quantum physics to Emmy, his cheeky German shepherd -- is a hoot, and has the singular advantage of making the mind-bending a little less traumatic when the going gets tough (quantum physics has a certain irreducible complexity that precludes an easy understanding of its implications); finally, third, it is extremely well-written, combining a scientist's rigor and accuracy with a natural raconteur's storytelling skill." -- BoingBoing