Teaching Multibody System Simulation: An Approach with MATLAB

Teaching Multibody Systems needs to cover the related theoretical concepts of advanced dynamics, the application of the necessary numerical methods in a sufficient depth, and needs to give students the opportunity to model and solve authentic problems on their own. The last step may only be done with the help of a computer. A variety of highly sophisticated computer programs are available (e.g., Adams), able to solve special problems from the area of Multibody Systems or even nearly every general type of engineering dynamics problem. The use of such software has some drawbacks for students however. There is a high risk to waste valuable time by learning how to use software that was not designed for educational use but was instead designed for large scale problems in industry. And, what is even worse, students do not really see how the software works, because the transition from the theoretical to numerical concepts is usually not visible in the software. To deal with this challenge, this paper presents a strategy based on the software Matlab, usually known by engineering students. The proposed method is based on doing symbolic manipulations for the derivations of the equations and on using numerical methods for the solution. The main idea is not to waste time and effort for getting the equations in a certain form needed for a computer solution, but to offer a procedure allowing students to easily use the equations as they are -known from the theoretical conceptand directly use them in Matlab. Furthermore the intention is not to be limited to simple 2D problems with just a few degrees of freedom but to offer the full range of a 3D Multibody System simulation with modelling, derivation of equations of motion, numerical solution of differential equations, calculation of static equilibrium as well as linearization and calculation of eigenvalues and eigenmodes. Based on a couple of small examples the paper gives a detailed introduction to the proposed method including all necessary equations and also the related Matlab code.