This book presents a three-dimensional model of the complete unicycle-unicyclist system. A
unicycle with a unicyclist on it represents a very complex system. It combines Mechanics
Biomechanics and Control Theory into the system and is impressive in both its simplicity and
improbability. Even more amazing is the fact that most unicyclists don't know that what they're
doing is according to science impossible - just like bumblebees theoretically shouldn't be
able to fly. This book is devoted to the problem of modeling and controlling a 3D dynamical
system consisting of a single-wheeled vehicle namely a unicycle and the cyclist (unicyclist)
riding it. The equations of motion are derived with the aid of the rarely used Boltzmann-Hamel
Equations in Matrix Form which are based on quasi-velocities. The Matrix Form allows Hamel
coefficients to be automatically generated and eliminates all the difficulties associated with
determining these quantities. The equations of motion are solved by means of Wolfram
Mathematica. To more faithfully represent the unicyclist as part of the model the model is
extended according to the main principles of biomechanics. The impact of the pneumatic tire is
investigated using the Pacejka Magic Formula model including experimental determination of the
stiffness coefficient. The aim of control is to maintain the unicycle-unicyclist system in an
unstable equilibrium around a given angular position. The control system based on LQ Regulator
is applied in Wolfram Mathematica. Lastly experimental validation 3D motion capture using
software OptiTrack - Motive:Body and high-speed cameras are employed to test the model's
legitimacy. The description of the unicycle-unicyclist system dynamical model simulation
results and experimental validation are all presented in detail.
