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*From*: Carl Mungan <mungan@usna.edu>*Date*: Thu, 27 Dec 2012 12:28:33 -0500

The intuitive way to handle this is to think about it in

angular momentum space. The contours of constant energy

are ellipsoids in this space. Let's choose one such

contour, i.e. let's choose a definite energy.

If the norm of the angular momentum is as small as possible

(consistent with the chosen energy) the angular momentum must

be at the short axis of the ellipsoid. If the norm is merely

/near/ the smallest possible value, the angular momentum must

be near the short axis. The geometry of spheres intersecting

with an ellipsoid guarantees it.

Similarly, if the norm of the angular momentum is at or near

the largest possible value, the angular momentum vector must

be at or near the long axis of the ellipsoid.

Now (!) consider the intermediate case. There are lots of

places the angular momentum vector could wander relative to

the ellipsoid. (In any inertial frame the angular momentum

vector doesn't wander at all, but the ellipsoid does, as

we re-orient the object. Alternatively, in a frame comoving

with the body, the ellipsoid stays fixed but the angular

momentum wanders.)

Thanks, that's a very helpful perspective to adopt and makes sense to me. Of course, now I wonder what Feynman would have said about it....

--

Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)

Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363

mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/

**Follow-Ups**:**Re: [Phys-L] intermediate axis theorem***From:*brian whatcott <betwys1@sbcglobal.net>

**References**:**[Phys-L] intermediate axis theorem***From:*Carl Mungan <mungan@usna.edu>

**Re: [Phys-L] intermediate axis theorem***From:*John Denker <jsd@av8n.com>

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