
Bibliography : Skateboard stability has been studied in depth by different scientists since the 70'. A mathematical model of the rider + board system has been built, then its behavior has been studied, in particular trough computer modeling.
You will find below links to the documents. I hope that you still have some good memories of your maths courses because it's a bit harcore !
Hubbard - Human Control of the Skateboard
Hubbard - Lateral Dynamics and Stability of the Skateboard
Hubbard - Optimal Human Control of an Unstable Vehicle in a Simple Tracking Task
Kuleshov - Mathematical model of the Skateboard
Kuleshov - Dynamics and simulation of the simplest model of skateboard
Kuleshov - MODELICA implementation of the skateboard dynamics