I give up
Monday 4 October 2021
The problem with the spiral is that the acceleration increases too rapidly since the field strength and the angle of the slope increase as the ball gets closer to the centre. To counteract the increase in field we would need to reduce the angle of the slope. This is not possible in 2D since the ball would the move away from the centre. Maybe it's possible in 3D?
It is. Here you can see the distance to centre getting less as the spiral radius gets more. This is when my brain starts to hurt. How on earth do I model the path of a ball travelling on a spiral track in 3D? I would go for an iterative model but how would I keep the ball on the track? Given the coordinates of the spiral maybe I could use suvat equations over a set of predetermined small steps, in this way I wouldn't have to wory about the forces needed to keep the ball on the track. No, I'm sorry I give up.