A Symbolic Approach to the Multibody Modeling of Road Vehicles

Abstract

This paper introduces MBSymba, an object-oriented language for the modeling of multibody systems and the automatic generation of equations of motion in symbolic form. MBSymba has built upon the general-purpose computer algebra software Maple and it is freely available for teaching and research purposes. With MBSymba, objects such as points, vectors, rigid bodies, forces and torques, and the relationships among them may be defined and manipulated both at high and low levels. Absolute, relative or mixed coordinates may be used, as well as combination of infinitesimal and noninfinitesimal variables. Once the system has been modeled, Lagrange’s and/or Newton’s equations can be derived in a quasi-automatic way, either in an inertial or noninertial reference frame. Equations can be automatically converted into Matlab, C/C++ or Fortan code to produce stand alone, numerically optimized simulation code. MBSymba is particularly suited for the modeling of ground, water or air vehicles; therefore, the mathematical model of a passenger car with trailer is illustrated as a case study. Time domain simulations, steady state analysis and stability results are also presented.