This simulation shows 2 balls on a roller coaster track. The 2 balls are connected by a
spring.
You can change the track shape by clicking a button below. You can drag either ball
with your mouse to change the starting position. Try changing gravity, damping or
spring stiffness.
The math behind the simulation is shown below. Also available are:
open source code,
documentation and a
simple-compiled version
which is more customizable.
 hump |
 loop-the-loop |
 circle |
 Lemniscate |
 oval |
 spiral |
Physics
This simulation is a variation of the Roller Coaster
with Spring, please see that page for more information on the physics and how the
simulation is done. The difference here is that the other end of the spring is attached
to another ball on the track, instead of being fixed.
We have 4 variables in this simulation:
- p1 = position on the track of ball 1 (measured by path length along the
track)
- v1 = velocity of ball 1
- p2 = position on the track of ball 2
- v2 = velocity of ball 2
The force equations for each ball are identical to that shown in the Roller Coaster
with Spring simulation except that the position of the "fixed end" of the spring is
replaced by the position of the other ball.
This web page was first published October 2002.