tangential riddle (was: expurgated version: "Negotiating" a curve)

["Carl E. Mungan" <cmungan@UWF.EDU>]

John Denker asked:

> Interesting tangential riddle:  You will find that for "most" problems you
> encounter, the two directions (AAA and CCC) in which the behavior is simple
> (almost scalar-like) will turn out to be perpendicular.  Is this a
> coincidence?  Is it because the problem-posers are artificially selecting
> simplified problems?  Or is there a law of nature at work here?  Exhibit a
> proof or a counterexample.

Aren't you really asking whether the principal axes must be orthogonal?
I would therefore say the answer is yes: start with some arbitrary 3x3
inertia tensor I. Then it is always possible to find a rotation matrix from
xyz to x'y'z' which will diagonalize I. But by construction x'y'z' is a
mutually orthogonal coordinate system.

Dr. Carl E. Mungan, Assistant Professor     http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL   32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu