TITLE: tippe top

NAME: Christian Friedl, Andre Wobst
COUNTRY: Germany

EMAIL: andre.wobst@physik.uni-augsburg.de
WEBPAGE: http://www.physik.uni-augsburg.de/~wobsta/tippetop/

TOPIC: slow motion
COPYRIGHT: I SUBMIT TO THE STANDARD RAYTRACING COMPETITION COPYRIGHT.
MPGFILE: tippetop.mpg
ZIPFILE: tippetop.zip
RENDERER USED: 
    povray 3.1


TOOLS USED: 

mpeg_encode, Fortran 77 & NAG mathematical library to get the motion data


CREATION TIME: 

about 1 hour (creating the motion data is not time expansive -- takes a minute
or so -- lets say 3%, than the rendering takes about 70%, rest is for
mpeg_encode)


HARDWARE USED: 

332 MHz 604e-X5 (IBM Workstation running AIX 4.3.3), the machine has 1.2 GB RAM
and four prozessors, but I did it serial (creation time wasn't an issue) and
the memory needed is negligible


ANIMATION DESCRIPTION: 

The animation shows the amazing motion of the so called tippe top. This is a
spinning top which has a stable equilibrium standing on a stem as long as it
spins fast enough. The animation starts with a fast spinning tippe top in its
natural position (like if you start a tippe top manually) and shows the
inversion to the position where the tippe top stands on the stem. After a while
it turns back towards the starting position.

The animation shows 10 seconds real time motion in proper geometry using 2000
pictures. On the webpage you can find a larger version (about twice the size
and twice the number of pictures). I can slow down the motion of the tippe top
as I wish, but you can't simply *see* why the tippe top behave like it does.


VIEWING RECOMMENDATIONS: 
    I use mpeg_play, but you may use whatever you want ...


DESCRIPTION OF HOW THIS ANIMATION WAS CREATED: 

The puzzling part of this work is the physical description of the problem tippe
top. You need a model with friction to get the inversion. Additionally you have
to have elasticity to get a numerically stable and more realistic behavior. The
elasticity is not shown in the animation, but you wouldn't be able to see any
difference (although the elasticity is large compared to most experimental
setups -- this leads to a quicker slowdown of the motion).

Beside analytical discussions of the equations of motion you can put the
differential equations into solvers. The result for one set of parameters and
starting values is shown in the animation. You can see how nice the model
reproduces the behavior of the tippe top. The render and animation task itself
is almost trivial. I hope, that's not the only important thing for this
competition ;-) ... (but I don't really care).

Further informations about the tippe top are available on the webpage.