Symbolic Modeling of Vehicles

This paper introduces to MBSymba, an object-oriented language for the symbolic modeling of multibody systems and the automatic generation of the symbolic equations of motion built on the foundation of a general-purpose computer algebra software. With MBSymba, the modeling procedure consists in the de- scription of the multibody system by defining objects (such as points, vectors, rigid bodies, forces and torques, plus some special objects) and the relationships among them (kinematic chains, constraints). The distinctive feature of MBSymba is the freedom left to the user to manipulate objects both at high and low level, to develop the model either in an inertial or non-inertial base, to employ either absolute or relative coordinates (and even to mix them), to select either a dependent on independent coordinates formulation and to define which variables are small (infinitesimal) and which are not. Once the system has been mod- eled, the derivation of the equations of motion can be performed in a quasi-automatic way, and the user has the possibility to use the Lagrange’s or the Newton’s approach, or to mix them. Additionally, the user may calculate, inspect and manipulate intermediate objects properties, such as potential and kinetic energy, as well as linear and angular momentum for bodies, power, generalized forces, etc. Finally, model equations as well as intermediate results may be converted into a Matlab, C/C++ or Fortan code to produce stand alone, numerically optimized simulation codes. As a case study, the development of a literature well known mathematical model of a four-wheeled vehicle is illustrated and discussed.