Stable and unstable curves in vehicle three-dimensional state space

In the field of vehicle system dynamics, revealing the dynamic characteristics of nonlinear vehicle models with high degrees of freedom is a key point in current research. In the classic 2-DOF (degrees of freedom) model, the dynamics is analysed and represented in two-dimensional state space. However, it is necessary to reveal the three-dimensional state characteristics of the system when analysing high-DOF vehicle models. The concept of equilibrium points in two-dimensional space will be extended to curves in three-dimensional space, including stable curves and unstable curves, which can qualitatively reveal the evolvement characteristics of the system under different control parameters. In addition, because the dissipation of energy method can quantitatively reveal the global dynamic characteristics of the vehicle, this paper combines the (un)stable curves in the three-dimensional space with dissipation of energy to better analyse the global dynamics characteristics and mutually verify the correctness of conclusions. In this paper, first, the connection between (un)stable curves and region boundary is established. Second, the theoretical analysis of relationship between dissipation of energy and phase trajectories convergence characteristics is perfected. Third, the static and dynamic characteristics of vehicle system are analysed. Therefore, this paper proposed the concept of stable and unstable curves to intuitively reveal the global dynamics characteristics and system evolvement characteristics in three-dimensional state space.