**Possible Capstone
Projects - Euler’s Disk**

Project subject area – dynamics of rotating bodies including friction.

**Introduction**

The rolling of a coin is a well-known mechanical behaviour,
featuring a coin precessing at ever shallower angle
and higher frequency until it suddenly falls down flat on a table (try that
again now!). A

A

A follow-up communication queried that suggestion,
indicating that the motion was largely the same in a near vacuum, and proposed
that contact friction was the dominant energy dissipation mechanism [3].
Stronger criticism still can be read in a letter that *Nature* rejected [4].

A model of the rolling and sliding friction has been included in the analysis [5] and included in a simulation code which can be downloaded from [6].

**Possible Capstone
Project Topics**

Capstone projects could be based on:

1) a review of the above controversy;

2) further theoretical analysis of the motion, including models of the contact friction;

3) further simulation of the motion by computer code;

4) experiments to parameterise rolling resistance (for various surfaces, disk edge radius, and force), to infer parameters for contact friction models, and to see if rolling resistance explains the energy loss.

Tackling any (or a mix) of these projects will require the complicated mathematics of solid body mechanics. Some lessons on rolling friction modelling will be learnt (if that is the dominant loss). Testing the disks, especially the commercial one, will be fun!

If this might interest you, please contact

**References**

[1] http://www.eulersdisk.com/, Tangent Toy
Company site, accessed on

[2] H.K.Moffatt
(2000) “Euler’s disk and its finite-time singularity”, *Nature* **404**, 833-834,
which can be downloaded from http://www.nature.com/nature/journal/v404/n6780/pdf/404833.pdf
(on

[3] Ger Van Den Engh, Peter Nelson & Jared Roach (2000) “Analytical dynamics: Numismatic gyrations”, *Nature* **408**,
540, which can be downloaded from
http://www.nature.com/nature/journal/v408/n6812/pdf/408540.pdf (on

[4] Runia
A. (2002) “Comment on Moffat’s Disk”, which can be
downloaded from http://tam.cornell.edu/~ruina/hplab/Rolling%20and%20sliding/Andy_on_Moffatt_Disk.pdf
(on

[5] P Kessler, O M O'Reilly
(2002) "The ringing of Euler's disk", *Reg. Chaot.
Dyn.,* **7** (1), 49-60, which can be downloaded from http://www.turpion.org/php/full/infoFT.phtml?journal_id=rd&paper_id=195
(on

[6] Milan Batista (2003-4)** **“Euler’s Disk Simulation Program”, which
can be downloaded from http://www.fpp.edu/~milanb/euler/