The dynamics of an articulated $n$-trailer vehicle

TL;DR

This paper derives and analyzes the equations of motion for an articulated n-trailer vehicle, revealing energy surface topology and stability of equilibria, with detailed dynamics for the single-trailer case.

Contribution

It provides a reduced mathematical model for articulated n-trailer vehicles and classifies their energy surfaces and equilibrium stability.

Findings

Energy level surfaces are (n+1)-tori.

Equilibria are classified and their stability analyzed.

Detailed dynamics described for the single-trailer case.

Abstract

We derive the reduced equations of motion for an articulated $n$-trailer vehicle that moves under its own inertia on the plane. We show that the energy level surfaces in the reduced space are $(n+1)$-tori and we classify the equilibria within them, determining their stability. A thorough description of the dynamics is given in the case $n=1$.