Applied Multibody Dynamics

People in charge

Dr.-Ing. Felix Boy (Lecture & Exercise)


The subject of multi-body dynamics is the systematic - and thus algorithmisable - description and analysis of the dynamics of systems of solid bodies. In industrial application, the simulation of multi-body systems (MBS) is indispensable, especially in the dynamic analysis of technical systems.

The lecture covers the relevant basics of the theory of the multi-body dynamics of rigid bodies. Starting with kinematics (especially 3D rotations), the dynamic equations in the form of momentum and angular momentum theorems, as well as the principle of principle of d'Alembert in the version of Lagrange are discussed. After a consideration of the theory of bonds/joints and some examples, the resulting system of differential-algebraic differential-algebraic system of equations and its properties follow. Finally, selected solution methods will be analysed and practical examples from practice are discussed.

In the exercise, which is held as a one-week intensive course, a 2D multi-body solver will be implemented in Matlab. Starting from object-oriented programming, all components of such a program will be implemented step by step. Furthermore, various realistic examples with the commercial MBS software MSC Adams will be examined and analysed.


  • Introduction and motivation: Formalisation of rigid body mechanics, application examples, lecture plan, recommended prerequisites, literature.

  • Vectors, coordinates, rotations: Representation of vectors in different coordinate systems, coordinate transformation, rotation matrices and rotation tensors.

  • Rotation in three-dimensional space: Euler/Kardan angles, Euler parameters, rotation tensor

  • Kinematics and kinetics: kinematic differential equation, momentum and angular momentum theorem.

  • Constraints: Bilateral constraints, distinction from unilateral constraints, typical constraint equations.

  • Equations of motion and DAE formulation: Principle of d'Alembert in Lagrange's version, definition of the descriptor form (DAE)

  • Differential algebraic systems of equations and their reduction to ordinary differential equations

  • Numerical methods of multi-body dynamics: Stabilisation and projection, Selected solvers

  • Application examples from practice

  • Implementation of a 2D multibody dynamics solver in Matlab

    • Overview of object-oriented programming in Matlab

    • Creating a programme structure for multi-body dynamics

      • Definition of location vectors, coordinate systems and bodies, as well as their representation

      • Forces, torques, given movements

      • Direct and inverse kinematics

      • Simulation of ordinary differential equations

      • Implementing algebraic constraints

      • Solving differential algebraic systems of equations

      • Application examples in MSC Adams

      • Definition of rigid bodies, import of CAD data

      • Creating coordinate systems, forces and impressed motions

      • Creation of simulations

      • Postprocessing and data export

Lecture announcement


The contents of Mathematics 1-3 and Engineering Mechanics 1-3 are required.

  • Lecture slides
  • Wittenburg, J., Dynamics of Systems of Rigid Bodies, Springer, 2010
  • Wörnle, Mehrkörpersysteme, Teubner-Vieweg
  • Führer, “Numerical Methods In Multibody Dynamics”, Springer, 2013
  • Shabana, A., Dynamics of Multibody Systems, Cambridge University Press, 2005

2 Lecture / 2 Excercise semester hours - 6 CP - Event number FB15-1098


Lecture : eLearning via Video + Consultation hours Monday, 6 - 8 pm
Excercise : Intentsive course in one week at the end of the lecture period

Skript: Lecture slides in advance on moodle, references in lecture

The course starts on April 15th 2024.


The Moodle course "Applied multibody dynamics" can be found in the offer of the department 15 at the Institute of Mechanics.