Bicycle science - how bikes work and the physics behind them

'Scientists have been puzzling over what makes bicycles balance since they were invented, back in the 19th century. In 2007, a group of engineers and mathematicians led by Nottingham University's J.P. Meijaard announced they'd finally cracked the mystery with a set of incredibly complex mathematical equations that explain how a bicycle behaves—and it turns out that gyroscopes are only part of the story.

According to these scientists, who used 25 separate "parameters" or "variables" to describe every aspect of a bicycle's motion, there's no single reason for a bicycle's balance and stability. As they say:

"A simple explanation does not seem possible because the lean and steer are coupled by a combination of several effects including gyroscopic precession, lateral ground-reaction forces at the front wheel ground contact point trailing behind the steering axis, gravity and inertial reactions from the front assembly having center-of-mass off of the steer axis, and from effects associated with the moment of inertia matrix of the front assembly"

Or, in simple terms, it's partly to do with gyroscopic effects, partly to do with how the mass is distributed on the front wheel, and partly to do with how forces act on the front wheel as it spins. At least, I think that's what they said!'

https://www.explainthatstuff.com/bicycles.html