From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 6 Aug 1999 11:09:36 -0500
Hi Ludwik-
I don't think that these characterizations are
either accurate or helpful.
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x) It is not true that a conical pendulum can be viewed as
a superposition of two "mutually perpendicular" simple
pendula oscillating with the same frequency and same
maximum spherical angle TET. Why not?
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I don't understand the question. Why on earth
should they be? It's like asking why isn't a marching
band like a french fried potato (somebody think up a
punch line to go with this question).
A mass hanging from a rigid (meaning fixed length)
string is a complicated system with two interacting degrees
of freedom. The linear and conical pendula are two different
linear limits of this system. The only thing that they have
in common is that both are gravity driven which implies
that the dynamics is independent of the mass of the system.
When I get some time, I'll try running the coupled
system on mathcad.
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First because the concept of perpendicularity does not
apply to curved lines.
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Say what? Lines of latitude and lines of longitude
on a sphere are curved and respectively perpendicular to
each other.
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography