From: | Simon Clarkstone <simon.clarkstone@...> |
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Date: | Thursday, April 28, 2005, 0:13 |

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.