Re: All you (n)ever wanted to know about the Ferochromon

Warning!  This email may be confusing, as it discusses _several_
mutually exclusive possibilities for the spiraling effect in
Ferochromon physics. ;->

# Velocity and displacement are *vectors*, with speed and distance
being the corresponding *scalars*.
# Approach and retreat are *motions*, but attraction and repulsion are
*"forces"* (which modify acceleration).

For much of this to be fun, the "lattice drag" would have to be quite
low, in order to see the effects.

If people really don't like this discussion being on CONLANG (though
*will* affect the vocab of the langs), say so, and I will attempt to
move the discussion onto the conworld list.

On 4/22/05, H. S. Teoh <hsteoh@...> wrote:
> BTW, out of curiosity, what do you have in mind w.r.t. how to approach
> creating equations that describe the Ferochromon? I've attempted this
> a few times but gave up because it just got way too complicated. The
> bit that requires constant force to remain in motion is easy, but I
> have a hard time coming up with precise equations that would predict
> such things as approaching objects spiralling inwards rather than
> collide head-on, or how objects in curved motion would be drawn
> inwards in the direction of the curve, etc..
Two possible interpretations:
either:
(1) (maybe not what you had in mind)
The direction of rotation depends on the perpendicular displacement
(including direction) of the objects (see fig. 1), so that objects
approaching head-on do not spiral.  Approaching causes rotation in a
hard-to-describe direction, (fig. 1), which then causes the objects to
be approaching each other head-on, so they stop spiralling.  Careful
with the equations, or you will get problems with objects that have a
small parallel displacement but large perpendicular displacement being
yanked towards each other, though they are far apart.

or:
(2) (sounds more like what you want, and much cooler)
Each realm has a "prime" direction that is distinguishable from the
others (see comment on lattices in a previous mail), even
distinguishable from its opposite direction.  The objects spiral in a
direction determined by a "right-hand" rule (see fig. 2a): make a fist
with your thumb out, then point your thumb towards the positive prime
direction.  Then your fingers curl the way that approaching objects
spiral.  This (arguably) isn't symmetric, but the right-hand rule
turns into a left-hand rule if you consider the *other* direction
along the prime axis to be positive.

The acceleration _could_ be determined by:
constant * ((relative displacement vector) cross-prod (prime direction
vector)) * (*other* object's mass) * (approach speed) * (1 / (distance
^ 2)),
though maybe you don't need to square the distance.  The relative
speed must be a scalar, with *opposite signs* for retreat and
approach.  Note: circling is neither retreating nor approaching.  The
cross product means objects approaching along the prime axis will not
spiral, which is *fun*, depending on the orientation of the local
ground w.r.t the prime axis.

(2) will not work if the relative speed cannot be negative (calculated
from: (velocity dot-mult displacement) / distance).  It could cause
two spiraling objects to be attracted by their own approach-induced
spiraling, forming a feedback loop that causes them to spiral into a
point (or single blob if incompressible).  One solution, indeed a
consequence of the above formula, is to have negative feedback, like
the EMF effect which limits motor speed: because motors obey the
reverse-hand rule to generators, the motion of the coil tries to
generate a current that always opposes the current already there.  The
other solution is a lot of "lattice drag", but that is boring.

Negative feedback would work analogously:
approach --(RH rule)--> clockwise spiral --(LH rule)--> repulsion -->
retreat --(RH rule)--> anticlockwise spiral --(LH rule)--> attraction
--> approach
(see fig. 2b)
This would probably not oscillate, but settle into a steady state: an
exponential, Archimedean, or logarithmic spiral, or the objects
drifting slowly apart.

(fig. 1: <http://www.dur.ac.uk/s.r.clarkstone/ferochromon/spiral1.png>
fig. 2: <http://www.dur.ac.uk/s.r.clarkstone/ferochromon/spiral2.png>
It's amazing what you can do in Paint :->)

BTW: I assume that you are using ddx/dtt = k * (f - dx/dt) for the
"drag" in simple 1-body motion, where f is a *velocity* that
corresponds to the local dynamons, and k is a constant.  Therefore,
objects tend to match the local "dynamon velocity", like a ball on a
moving walkway e.g:
<http://news.bbc.co.uk/1/hi/world/europe/3001182.stm>.  With no motive
fields around, the speed decays exponentially.)

I am sorry if any of the above is incomprehensible, but it is early in
the morning and I should be going to bed.