Introduction to Multibody Dynamics

Prof. Dr.-Ing. Hartmut Hetzler (Lecture)          Mitja Rosenboom, M. Sc. (Exercise)

The subject of multibody dynamics is the systematic - and thus algorithmisable - description and analysis of the dynamics of systems of solid bodies. In industrial practice, the simulation of multi-body systems (MBS) is indispensable, especially for the dynamic analysis of technical systems. As part of of the lecture, the basics of kinematics and kinetics of the individual rigid body are first repeated and deepened. Based on this, the description of systems of rigid bodies is developed, whereby the representation as ODE as well as DAE is treated. Basic aspects of numerics are presented for both variants. The lecture concludes with an outlook on analytical principles as well as on the treatment of MBS with the help of modal reduction. The analytical basics are deepened in exercises. In parallel, simple examples are programmed in software such as Matlab / Octave or possibly wxMaxima.

• Introduction & Motivation
• Kinematic Basics: Notation, Coordinate Systems, Finite Rotations, Kinematics of Rigid Bodies
• Kinetic Basics: Law of Conservation of (Angular) Momentum, Work and Law of Conservation of Energy
• Kinematics of Multibody Systems: Degrees of Freedom, Bonds, Systems with Tree Structure, Systems with Constraints
• Basics of numerical Integration of ODE and DAE Systems
• Lagrange-d'Alembert principle, Jourdain principle, Gauss's principle of least constraint
• Basics of Elastic MBS