Multi-body Simulation

Lecturer (assistant)
Duration2 SWS
TermSommersemester 2019
Language of instructionEnglish
Position within curriculaSee TUMonline
DatesSee TUMonline


Course criteria & registration


At the end of the course the students are able to describe a mechanical system as a classical multibody system. The students apply an abstract and modular formalism for the derivation of the respective equations of motion in the planar as well as in the three-dimensional case. Furthermore they are able to integrate flexible bodies modeled by the Finite Element Method into the multibody system. Beside the derivation of the equations describing the dynamics of the system, the students know several numerical time-integration schemes for linear and non-linear constrained systems.


Multibody systems are technical systems consisting of different rigid or flexible bodies that are interconnected. The connections may be modeled with classical force laws (massless springs and dampers, actuators, contact) or realized by kinematical constraints, e.g. joints. 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. Embedding the Finite Element Method (FEM) into the framework allows to concurrently simulate rigid and flexible bodies and their interactions. Topics: 1. Dynamics of rigid bodies (Newton-Euler equations, Lagrange equations, Hamilton principle, ...) 2. Relative kinematics in space (spatial rotations, ...) 3. Assembly of a multibody system (link forces, constraints, ...) 4. Considering flexible bodies 5. Time integration (Newmark integration scheme, linear/nonlinear systems, constraints, ...)


From lecture Engineering Dynamics: sections "Analytical dynamics" and "Dynamics of rigid bodies"

Teaching and learning methods

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


After the lecture period, there will be a written or oral (depending on number of participants) exam.

Recommended literature

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