Integrated Vehicle Dynamics and Control

1Basic Knowledge of Vehicle System Dynamics

1.1 Traditional Methods of Formulating Vehicle Dynamics Equations

Traditional methods of formulating vehicle dynamics equations are based on the theories of Newtonian mechanics and analytical mechanics. Some of the definitions used in dynamics are presented first.

1. Generalized coordinates

   Any set of parameters that uniquely define the configuration (position and orientation) of the system relative to the reference configuration is called a set of generalized coordinates. Generalized coordinates may be dependent or independent. To a system in motion, the generalized coordinates that specify the system may vary with time. In this text, column vector is used to designate generalized coordinates, where n is the total number of generalized coordinates.

    In Cartesian coordinates, to describe a planar system which consists of b bodies, coordinates are needed. For a spatial system with b bodies, (or ) coordinates are needed.

    The overall vector of coordinates of the system is denoted by , where vector q_i is the vector of coordinates for the i