Peter Dong - Les Phys song RIGID BODY ROTATION | Текст песни

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#2 RIGID BODY ROTATION
Think of a free symmetrical top—I-one the same as I-two—
Spinning around x-three-hat nonstop. Euler’s equations tell you
That I times omega-one-dot plus I-three minus I times omega-three-two
Is zero, so I-three-omega is always a constant whatever you do.
This produces a simple harmonic effect, which means omega revolves
‘Round about x-three-hat as we’d expect, and our equation resolves
To show that L traces a conic with faces precessing around x-three-hat.
But I’m sure you won’t have any problem with that.
Now let’s see how this behaves in space, so our equation for L
Shows very plainly it is the case—principle axes will tell—
That I times omega-one times x-one-hat plus omega-two x-two-hat plus
I-three times omega-three times x-three-hat gives you L without all of the fuss.
So we see that the vectors all lie in a plane—L is a constant, you see,
Omega and x-three-hat will remain rotating ‘round x-sub-3
While omega-tilde’s direction is still the direction that L’s pointing at.
But I’m sure you won’t have any problem with that.
GEORGI: Yes, a question.
SMART GUY (OR GIRL): So is angular momentum just a convenient way to solve problems, or
does it have any deeper significance?
GEORGI: That’s a good question. Classically it is nothing more than a convenient device, but in
particle physics—which is my field, of course—angular momentum is something more
meaningful. There you have the concept of spin, a kind of angular momentum intrinsic
to all particles, and it’s really amazing how much spin affects the interactions between
particles.
Ions and muons and pions and gluons and bosons and leptons and quarks
And hadrons and photons and tauons we note on selected neutrinos with internal torques
Because physics has a music, a rhythm and a rhyme.
But that’s something other; we still have to cover nutation, and we’re almost out of time.
Now what if theta varies a bit? Phi-dot of t can be small.
This perturbation that we permit shows, as I’m sure you recall:
I-phi-dot-dot sin theta minus omega-three theta-dot I-three is naught.
So omega-s times omega-n-squared minus omega-n-squared-phi-dot
Gives the triple derivative phi by dt. Now we can solve this for phi.
Set the initial conditions to see how these equations apply:
We find that our theta and phi indicate a precession and not something flat.
But I’m sure you won’t have any problem with that.
Well, we didn’t get to everything because we stopped to chat,
But I know you’ll find, if you keep in mind what I’ve said today, it’ll be okay,
‘Cause I know you won’t have any problem with that.

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