TITLE: Egg-ovoid rolling down an inclined plane
QUESTION [14 upvotes]: 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), or,
a bit more formally,
"The Mathematics of Egg Shape" (PDF download) by Yutaka Nishiyama, from which I
copied this figure (and the one below):
           
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!

REPLY [4 votes]: This paper https://jeb.biologists.org/content/221/19/jeb178988 contains an experimental investigation of egg rolling. Theoretically, it seems "the relationship of egg shape to egg movement (e.g. rolling) is an understudied topic".