# Modelling and Stability Analysis of Articulated Vehicles
## 1 Introduction  
Articulated vehicles with small steering radius and positive maneuverability are extensively used in mining, construction, forestry, emergency rescue, and other fields [1, 2]. Articulated vehicles consist of two separate front and rear vehicles and an articulated steering device connecting the both vehicles. This particular form of construction and steering results in underdeveloped stability, specifically at high speed, and the snaking instability phenomenon will occur [1, 3]. This situation increases the operating burden and danger for drivers and limits the speed and efficiency of articulated vehicles. Therefore, the factors influencing the stability and snaking instability of articulated vehicles should be studied. Numerous studies examined the instability of articulated vehicles, and two research methods for the stability analysis of these vehicles are currently available. The first approach assumes that vehicles travel at a constant speed, obtains the corresponding characteristic equations by linearising the vehicle dynamics model and analyses the vehicle state using the eigenvalue method [4, 5, 6]. The other approach uses numerical integration methods to obtain responses to some arbitrary inputs [7, 8]. The majority of the related studies have used the first method for the corresponding analysis of articulated vehicles. [PERSON] and [PERSON] [9] studied the steering system, simulation model and stability criteria to gain an improved understanding of the closed loop stability characteristics. [PERSON] and [PERSON] [5, 10] firstly invoked the eigenvalue method to judge the stability of articulated vehicles. Snaking critical velocity is obtained when the real part of the eigenvalue is positive. He analysed the correspondence between articulated vehicle jack-knife and snaking. [PERSON] [4, 11] provided an overview of lateral stability analysis. The influence of some vehicle structure parameters on the stability of articulated vehicles is analysed. [PERSON] [12, 13] studied the critical speed of articulated vehicles' hydraulic steering systems with differenthydraulic moduli of elasticity. [PERSON] [3] studied the snaking mode under different conditions by the articulated angle. [PERSON] and [PERSON] [14] analysed the effects of air content in the fluid and vehicle drive form on the articulated angle. Eigenvalue analysis is limited to linear or linearised models and is considered valid near the point of linearization [15]. [PERSON] [6] built a scaled test vehicle model, and verified the practicality of the stability analysis method based on the linearised kinetic model. Stiffer steering leads to high frequency of snaking, and flexible suspension negatively affects snaking stability [16]. [PERSON] [8] constructed a nonlinear vehicle dynamics model and used an integration method to derive an analytical periodic solution of the system in the neighborhood of the critical speed. [PERSON] [17] showed that elastic torsional suspension can improve the roll stability of vehicles, but the directional stability at high speed of vehicles with suspension is poorer than that of vehicles without suspension. [PERSON] and [PERSON] [18] analysed the limited perception of driver, which has insensitivity zones of the lateral and angular locations. Drivers rely heavily on rotational motion and their senses to prevent vehicles from snaking; hence, drivers have a significant impact on vehicle stability. The current study constructs a nonlinear articulated vehicle dynamics model and hydraulic steering system model. The nonlinear dynamics model, stability analysis models and equations of state are obtained using Newtonian mechanical equations relative to the previous generalised force approach, specifically by deriving the Lagrange equations. The characteristics of snaking are investigated, and the causes of snaking are analysed using multiple vehicle status parameters. The factors influencing the stability of articulated vehicles are analyzed, and the influence of some new factors are specifically studied.