Stability of uniform rectilinear motion of a tractor with two trailers

This paper investigates the stability of uniform linear motion of a tractor followed by two identical single-axle trailers. It is shown that in addition to the articulated connection of the first trailer with the tractor and the second trailer with the first one, the mechanical compliance of each coupling should be taken into account when identifying the conditions of motion stability for the system. The Appel equations are used to develop a mathematical model of the motion of the system with two nonholonomic constraints in a linear formulation. Dimensionless problem parameters, dimensionless generalized coordinates, and dimensionless time are introduced to represent the mathematical model in the most compact and convenient form. By analyzing the characteristic equation of the sixth order using the D-decomposition method and the Liénard-Chipard criterion, the stability motion regions are constructed on the plane of two dimensionless parameters for different values of the other two dimensionless parameters. The obtained data are compared with the solution of the motion stability problem for a tractor with one trailer. The results allow determining the qualitative and quantitative features of the derived solution. The conclusions drawn in this paper are of interest not only from a theoretical point of view, but can also be useful for practical applications.