The stability of the bicycle (2006)
scitation.aip.org
scitation.aip.org
http://www.control.lth.se/media/Staff/KarlJohanAstrom/Lectur...
To those of you who are fans of Randall Munroe's What-If I heartily recommend the out of print classics The Inventions of Daedalus and its sequel The Further Inventions of Daedalus which are in a losely similar vein.
Last I heard (a few years ago) he was still alive and a documentary largely about his ingenious "perpetual motion" machines was made. I hope he's still hearty but fear he may have passed.
minutephysics had a great video about this too:
How Do Bikes Stay Up?: https://www.youtube.com/watch?v=oZAc5t2lkvo
I think that this is the current status, knowing that the bike does not fall by the simultaneous combination of several factors. When analyzing the problem mathematically, it can be found that there are additional stability factors that do not even have direct physical meaning.
http://socrates.berkeley.edu/~fajans/Teaching/MoreBikeFiles/...