Re: historical question

[John Denker <jsd@AV8N.COM>]

Larry Smith wrote:
> Did Newton do much with rotating rigid bodies (torque, angular momentum,
> moment of inertia, etc.), or were those later developments?

Yes and no.  Newton definitely stomped all over the Kepler
problem.  Kepler's equal-area law can be seen as a special
case of conservation of angular momentum.

But the special case (equal-area orbits) doesn't necessarily
give you the general case (conservation of angular momentum).

Also the special case of D=2 (planar orbits and/or rotation
around a single, fixed axis) is much simpler than the full
D=3 formulation.

> If later, who
> were the leading lights in the explication of the mechanics of rotating
> rigid bodies?

The usual suspects are Lagrange and Hamilton.  A little
later, Maxwell studied the precession of a slow, heavy top.

> The cross product hadn't been invented in Newton's day.

Nor indeed until much, much later.

Hamilton knew a thing or two about classical mechanics,
and a thing or two about quaternions as early as 1843,
but despite years of effort he couldn't explain the
combination in terms others could understand:
  http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html

Some remarks about the next chapter of the story (cross
product versus wedge product) found at:
http://www.euclideanspace.com/maths/algebra/clifford/GeometricAlgebraRepresentationalTool.htm

> > Between 1891 and 1894, in the journal Nature, long letters defending
> > various notions can be found between the proponents of both sides of
> > the representational conflict. .... Anyone interested in what a 19th
> > century flame war looks like is encouraged to do a little digging in
> > the library for volumes 43 through 46. Gibbs first letter was
> > published April 2, 1891 and Tait's first response appeared four weeks
> > later.

If you were ever wondering whether Maxwell was smart or
not, consider that he did his work on electrodynamics and
on precessing tops without cross-product or wedge-product
technology.  Ouch!


> Or maybe torque goes back to Archimedes and his levers.

Yes ... but again the special case (levers in the plane) doesn't
necessarily give you the general case (torque vector).

====

I have no idea when or by whome the law of conservation of
angular momentum was first codified.