The Physics of Motorcycles and Fast Bicycles : Lean, Stability and Counter-steering

TL;DR

This paper develops a comprehensive nonlinear model of motorcycle and fast bicycle dynamics, demonstrating unconditional stability and providing a quantitative explanation of counter-steering behavior.

Contribution

It introduces the first detailed nonlinear equations for motorcycle and fast bicycle motion, analyzing stability and modeling counter-steering quantitatively.

Findings

Unconditional stability of motorcycle motion at all tested speeds.

Accurate calculation of lean angles during turns.

Quantitative model explaining counter-steering phenomenon.

Abstract

In this work I will obtain the system of nonlinear equations that correctly describes the motion of motorcycles and fast bicycles (above 30 km/hr) for the first time in literature. I will use it to calculate the lean angle during a turn and prove that the motion of the vehicle is unconditionally stable at all operating speeds under consideration. I will then employ it to give a quantitative model of counter-steering - the phenomenon by which a turning mobike first goes the wrong way and then starts going the right way.