I am seeking a mathematical analysis of an egg-ovoid rolling down an inclined plane, 
for pedagogical reasons.
It is well-known folk lore that the shape of an egg prevents it from rolling away from
the mother's nest, e.g., the article
"Why are eggs egg-shaped?" ([link][3]), or,
a bit more formally,
"The Mathematics of Egg Shape" ([PDF download][1]) by Yutaka Nishiyama, from which I
copied this figure (and the one below):
<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;![Egg Fig][2]<br />
If anyone has seen a mathematical analysis of this phenomenon, more precise than observing
that an egg-ovoid fits inside a cone, and a cone rolls a circular arc, I would appreciate
a pointer.  Thanks!
<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;![Egg Fig][4]<br />


  [1]: http://www.osaka-ue.ac.jp/zemi/nishiyama/math2010/egg.pdf
  [2]: https://i.sstatic.net/WqA2N.jpg
  [3]: http://www.bigsiteofamazingfacts.com/why-are-eggs-egged-shaped-and-how-does-the-ovoid-shape-of-an-egg-prevent-it-from-rolling-out-of-the-nest
  [4]: https://i.sstatic.net/17Ymo.jpg