Re: Sodaplay: Tacoma Narrows resonator

[Leigh Palmer <palmer@SFU.CA>]

>  >Resonance has several meanings in common parlance. In physics resonance
> > refers to only one phenomenon, the one which is called sympathetic
> > vibrations in common parlance!
>
> Do the purveyors of Quantum Mechanics agree with this dictum??
>
> If so, I'd like to hear about the 'sympathetic vibrations' that occur
> on the sub-atomic realm.

I can't really come up with a good example in that realm, but I have
many in the astronomical realm, where "resonance" has a closely
related meaning. From a recent bit of my own writing (attached).

Leigh

The term "resonance" is widely used (and misused) in scientific
parlance. Its meaning often depends upon context. In the context of
solar system celestial mechanics resonance refers to a number of
different phenomena in which periodic or quasiperiodic systems are
coupled, and in which that coupling produces a commensurability in
the periods of the systems. That is, the coupled phenomena have
periods which are related by ratios of small whole numbers.

There are many examples of such resonances to be seen in the solar
system, and there is even a common resonance phenomenon to be seen
outside our system, in close binary stars. The mechanisms by which
such resonances are established and maintained are, for the most
part, understood at least qualitatively.

The most widely known of these phenomena is seen in the Moon, which
rotates once on its axis for each revolution it makes with respect
to the Earth. As a consequence the Moon always keeps its same face
toward the Earth or, more properly, one never sees most of the
backside of the Moon from Earth. This 1:1 ratio of periods is called
synchronous rotation of the Moon. The Moon does not rotate with
respect to the earth. This kind of resonance, between rotational and
orbital periods, is called a spin-orbit resonance.

Another kind of resonance is found between coupled orbits. The
average orbital period of each asteroid in two groups known as
"Trojans" is the same as the orbital period of Jupiter. This
phenomenon is known as an orbital resonance or else an orbit-orbit
resonance, and in this case it is a synchronous orbital resonance.
Synchronous orbital resonances are also seen in circumstances in
which the coupled orbits are those of more evenly matched objects
such as the Saturnian satellites Janus and Epimetheus.

Neither sort of resonance need be synchronous. It was once believed
that the planet Mercury was in a synchronous spin-orbit relationship
with the Sun. This false impression was founded in the difficulty
which Earthbound optical astronomers encountered in observing
Mercury, which seldom appears separated very far from the Sun, and,
likely, in their familiarity with the phenomenon of synchronous
rotation. However, measurements done using radar in the sixties
indicated that the planet does rotate with respect to the Sun.
Refinements in these measurements have since shown that Mercury is
in a 3:2 spin-orbit resonance. Mercury's orbit is highly eccentric,
which favors the establishment and maintenance of such a resonance.
It rotates one and one half times between successive perihelion
passages.

There is a group of asteroids (the Hilda group) in or near resonance
with orbital periods near 2/3 that of Jupiter, and Pluto's orbital
period is 3/2 the orbital period of Neptune, a resonance which,
paradoxically, minimizes their coupling. Minimization of coupling
between interacting systems is a commonly seen characteristic when
sharply defined resonances occur in other, non celestial mechanical,
physical contexts.

Perhaps the most intricate resonance of all is seen among the three
Galilean satellites Io, Europa, and Ganymede. These bodies revolve
around Jupiter with orbital periods PI, PE, and PG, respectively,
related such that

               1     1     1
              --- - --- + --- = 0
              PI    PE    PG

As a consequence of this relation whenever two of these satellites
are in conjunction the third is always at least 60° away*.The
overall result of this simple relation is that there is a
periodicity in the relative motion of these satellites. The period
of this motion, Prel, is just the interval between successive
conjunctions of Ganymede relative to Europa, the synodic period of
these satellites. Prel may be calculated from the relation

               1     1     1
             ---- = --- - ---
             Prel    PE    PG

Prel is 169.22225111 hours.

*Whenever Europa and Ganymede are in conjunction as seen from
Jupiter, Io is in opposition to the pair. Whenever Io and Europa are
in conjunction, Ganymede is either in opposition or else in
quadrature with respect to the other two satellites. This means that
whenever two adjacent satellites are in conjunction and thus
interacting most strongly, the third satellite is at least 90° away,
reducing three body coupling to a minimum so long as the resonance
is maintained. Whenever Io and Ganymede are in conjunction, a weaker
coupling than occurs when adjacent satellites are in conjunction,
Europa is at least 60° away.