Multi-body Simulation (Lecture)

LecturerDaniel Rixen [ML], Arne-Christoph Hildebrandt, Michael Häußler
Allocation to curriculumSee TUMonline
Offered inSommersemester 2016
Semester weekly hours2  
RegistrationSee “Course criteria & registration”

Objective (expected results of study and acquired competences)

At the end of the course, students are able to classify a real mechanical system as a classical multibody system. The students apply an abstract and modular formalism for the derivation of the respective equations of motion with absolute and relative coordinates. The students evaluate respective classical numerical integration methods according to their advantages and disadvantages. The students summarize the components and difficulties of contact mechanics models and integration. The students use Matlab for the implementation of the mentioned methods.


Multibody systems are technical systems consisting of different rigid or elastic bodies that are interconnected. The connections may be modeled with classical force elements like spring-dampers or realized by kinematical constraints, e.g. joints. Moreover, frictional contacts between bodies can be modeled using unilateral constraints and Coulomb-friction. In the meantime multibody simulation programs are well established and can be found in a variety of industrial sectors, for example in aeronautical engineering or in the automobile industry. In consideration of initial and boundary values, a multibody simulation provides the transient motion of the bodies as well as the forces and moments acting in the connections between bodies. Besides the Finite Element Method (FEM), the multibody simulation is an important tool for numerical computations in mechanical engineering. The basic aim of the lecture “Multibody simulation” is to give access to the computer aided simulation of dynamical systems. Planned topics:
1. Imbedding in mechanics / applications
2. Equations of motion with Newton-Euler in descriptor- and state space form (Matlab examples)
3. Numerical integration (one-step- and multi-step schemes / order / stability / geometry / step-size control / Matlab examples)
4. DAE integration (index / drift / stabilization)
5. Nonsmooth MBS (contact kinematics, contact search and contact laws / event-driven integration and timestepping methods / Matlab examples)
6. Flexible MBS / model order reduction / Co-simulation / optimal control

Previous knowledge expected

Lecture Advanced Engineering Dynamics - section 'formalisms': The students use an estabilshed formalism for the derivation of the equations of motion of mechanical models.

Teaching and learning method (delivery of skills)

presentation (tablet), slides, lecture, Matlab examples, animations/visualisations, case studies

The cognitive process is achieved by developing the methods of multibody simulation step-by-step on the tablet. The students learn the implicit process knowledge by "thinking loudly". Exemplary, practical problems are discussed as well as implemented and visualized with Matlab. The students get the lecture notes section-by-section for their respective preparation and wrap-up. 2- or 3-times the lecture is substituted by a lab in the computer pool of the institute. In small groups, case studies are analyzed and evaluated as well as methods of the lecture are implemented in Matlab by the students.

Assessment (exam method and evaluation)

After the lecture period, there will be a written exam. Due to short questions classical methods of multibody simulations have to be summarized and applied to examples. Short case studies and Matlab examples have to be analyzed and evaluated concerning the applied classical methods of multibody simulation. Methods for contact mechanics have to be summarized due to short questions.


preparation and wrap-up with slides, lecture notes, case studies and Matlab examples; established further literature can be found in the lecture notes.