Some New Remarks about the Dynamics of an Automobile with Two Trailers

Abstract

The goal of our paper is to complete some results presented by Craioveanu et al. (1998) concerning the nonlinear stability of the equilibrium states of the car with two trailers’ dynamics. In addition, the Lax formulation, numerical integration via Lie-Trotter, and Kahan’s integrator for these dynamics are presented.

Stabilization of a nonlinear control system on the Lie group SO(3)×R3×R3

“…For a Hamilton-Poisson system, like the considered system (1.1), the energy-methods are used in order to establish stability results (see [2] or [4] for instance). New challenges appear when the energy-methods are inconclusive.…”

A Drift-Free Left Invariant Control System on the Lie Group SO(3)×R3×R3

“…An important class is the control problems on matrix Lie groups due to the possibility to study them from Poisson geometry point of view. Many dynamical systems have as configuration space a Lie group, such as (3) for the spacecraft dynamics (see [1]), 2 × (3) for the ball-plate problem (see [2]), 5 for the dynamics of the car with two trailers (see [3]), (2, ) for the Maxwell-Bloch system (see [4]), or (2, ) × (2) for the dynamics of a rolling penny (see [5]).…”