Re: Periodic motion vs. oscillation

[John Denker <jsd@AV8N.COM>]

Robert Cohen wrote:
> What, if any, is the difference between periodic motion and
> oscillations?

For starters, oscillations need not be periodic.  I get
hundreds of hits from
  http://www.google.com/search?q=chaotic-oscillation
some of which look rather interesting.

BTW everybody ought to read Glieck's book
  _Chaos: The Making of a New Science_

> For example, the motion of the earth around the sun is an example of
> periodic motion.  But is it an example of an oscillation?

1) Note that the earth's motion is not _exactly_ periodic ...
we just call it periodic by way of approximation / idealization.

2) In the ideal case, periodic orbital motion in the XY plane
can be decomposed into two oscillations: one along the X axis,
and one along the Y axis (90 degrees out of phase).

  It is a time-honored homework problem to calculate the
  period of oscillation of a rock dropped into a tube that
  passes diametrically through the center of the earth.
  For simplicity, imagine a homogeneous nonrotating Earth,
  and no friction.

So I guess to my ears "oscillation" has a connotation of
one-dimensional excursions (as a function of time and a
function of one or more independent variables).  Example:
Chladni-type oscillations of a metal plate.  I'm not
dead-set against higher-dimensional excursions, but I
can't think of an example that sounds right.

Consider a perfectly balanced wheel, e.g. a perfect disk
spinning on its axis.  I would prefer not to say that it
is oscillating.

OTOH consider a perfectly balanced barbell-shaped rotor.
I might say that there are some oscillatory components
to the motion.

Also it is reasonable to say that Venus in its orbit oscillates
above and below the plane of the ecliptic.

> I thought that an oscillation is when something is forced back to some
> equilibrium position

I reckon that's necessary, but far from sufficient.  It
is necessary in the sense that oscillation by definition
means "back and forth", and any physical motion will
involve forces, so oscillators will be "forced back".

It is not sufficient since a grossly overdamped system
will be "forced back" but will not oscillate.  (It may
be instructive to think about the transition from
oscillatory to non-oscillatory behavior as a function
of damping.)

====

BTW an electrical oscillator does have "forces" if you
think about it in the right way.  First, write down
the Lagrangian.  Then pick a coordinate;  the physics
doesn't care whether you pick charge or flux as the
coordinate.  Then turn the crank to find the momentum
that is dynamically conjugate to your coordinate.
Define force = (d/dt)momentum.

Working out the canonical mechanics of an electrical
circuit is a great exercise ... shedding light on the
methods of classical mechanics *and* shedding light on
the operation of the circuit.  Once upon a time I did
this as a self-assigned exercise, and it led (a couple
of years later) to one of the most important papers I
ever wrote (in collaboration with Bernie Yurke).

The canonical mechanics of a piano string is in the
same category.  Highly recommended.