The comfortable roller coaster -- on the shape of tracks with constant normal force
Mathematical Physics
2015-05-19 v1 math.MP
Classical Physics
Abstract
A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.
Keywords
Cite
@article{arxiv.1007.1394,
title = {The comfortable roller coaster -- on the shape of tracks with constant normal force},
author = {Arne B. Nordmark and Hanno Essen},
journal= {arXiv preprint arXiv:1007.1394},
year = {2015}
}
Comments
10 pages, 4 figures