Reply To: Physics Nobel to Big Bangers

[vansig]

benf wrote: I see what you mean, Vansig. I’ve looked it up in Wikipedia. The problem for me is adjusting the coil (paths) manually to make it circular will be very difficult. I can key in a math formula in the 3D program I’m using, which I’ve never done before. I’m searching the web for the handy formula that will just generate the correct coil, but haven’t found it yet.

ok.
let the toroid’s major diameter = D, and its minor diameter = d;
let the object’s centre be at (0,0,0);
trace a virtual path, P, having velocity W radians/s around the centre, at radius D/2,
such that at time t,
P(t) is a cartesian-coordinate point, whose value is the ordered triple, ( D·cos(Wt)/2, D·sin(Wt)/2, 0 );
this is a reference circle.

Trace a solid path Q, having velocity w radians/s around P, such that at time t,
Q(t) = ( D·cos(Wt)/2 + d·cos(Wt)·cos(wt)/2, D·sin(Wt)/2 + d·sin(Wt)·cos(wt)/2, d·sin(wt)/2 ).

i haven’t tested this, but i think it will do.