freecounterpoint: More Larmor Precession!

Tuesday, March 06, 2007

More Larmor Precession!

11 comments:

My Frontier Thesis said...: Pretend like you have to explain this to a historian or humanities student. Okay, go ahead:; 3/06/2007 11:28 AM
Mr roT said...: Hmmm, y'know how a spinning gyroscope, when put on a table not vertically will sweep out a cone with its axis? That's called precession.
If you have a spinning charged massive ball, floating in space, in an external magnetic field B, the spinning charge will make its own (current and thus) magnetic field and the two fields will make a torque on the ball by their having to coexist.
That torque is analogous to the torque exerted on the gyroscope by its support not being directly below its center of mass (remember I said the gyro isn't vertical).
So the spinning ball precesses and its axis fills out a cone in space with its point at the center of the ball. I can describe the motion of the gyro by imagining a point in its axis and watching it traverse a horizontal circle in space. The gyro is pinned to the table at its point of contact and so that is the point of the cone. The ball is similar.

Now imagine that I can rotate the external magnetic field so that IT goes round in a circle. Now let the spinning charged ball free in that.
At each instant, the ball feels like it's in the static magnetic field and so precesses, but an instant later, the magnetic field is different and so the ball has to adjust its precession to match.

What happens is difficult to talk through. It's better at this point to write down a differential equation modelling the motion. Solving it, however, is difficult. I wrote a Mathematica program that makes the computation and Mel figured out how to get it to output movie .gif

What you see is the point traced out by that point in the axis of the gyro-ball.

Couple reasons it's interesting: Notice that though the magnetic field repeats itself in time, the motion does not, but evolves chaotically.; 3/06/2007 1:26 PM
Mr roT said...: Another reason this is of interest is that NMR works on the same principle; the atomic nucleus behaves as if it were a massive, charged, spinning ball.; 3/06/2007 3:58 PM
Arelcao Akleos said...: For doing without the mathematics, JJ, that was a bravissimo explanation. But next time try it with the vocabulary of Mr. Roger's Neighborhood....in rhyme.; 3/07/2007 8:13 PM
Mr roT said...: Thanks AA. Did you like the animation?; 3/08/2007 1:22 AM
My Frontier Thesis said...: Thanks, JJ. Only now did I get to read this. I'll have to give it another re-read after morning coffee tomorrow. However, the gyro is making more sense now (in a chaotic sort of way).; 3/08/2007 1:25 AM
Mr roT said...: When I wrote 'coexist' above I was thinking of minimizing energy. More familiar to your experience would be the force that two magnets feel when they are close to one another. They push toward an antiparallel arrangement so that each's north pole is close to the other's south pole. That force is what the spinning ball feels (since its current induces a mag field) and its push to align its field antiparallel to B is what gives rise to the precession which is a gyro phenomenon.
I hope that's clearer.; 3/08/2007 2:01 PM
My Frontier Thesis said...: ...so when are you gonna be able to deliver the mathematical specs on the anti-gravity (or magnetic) gyro device needed for floating cars?

Make Coanda obsolete?...

Also, is there a way to plug in a sort of "cam-shaft" (best analogy I can think of right off) to stabilize the spinning magnetic gyroscope, something that would also account for the torque applied to the spinning charged massive ball that stems from the magnetic field of space?

If I understand this right, I see all sorts of existentialist analogies and metaphors (how individual objects act and react, and how the environment imposes a measure of its inanimate will on that object, ad infinitum).; 3/08/2007 3:09 PM
Arelcao Akleos said...: The animation was very neat......is this something you were doing for fun or for a class presentation?; 3/08/2007 3:27 PM
Mr roT said...: Kinda a job talk. I'll email you something.; 3/08/2007 4:40 PM
My Frontier Thesis said...: There's even pattern within chaos. Real cool, JJ.; 3/08/2007 9:06 PM

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