Open to students
of all nationalities having a bachelor degree

  • mechanical
  • transport
  • electro

Unique in Europe
two years master studies

  • high level of technical studies


  • combined with language studies

International cooperation
of six renowned universities

  • CTU in Prague
  • HAN
  • ENSTA Bretagne


  • ITB Bandung
  • TU Chemnitz
  • IFP Paris


Double degree
from two countries

  • depending on chosen universities and specialisations


  • Study stay in at least 2 countries

Eight specialisations
offered in the second year of study

  • Advanced Powertrains
  • Design of Vehicles
  • Alternative Powertrains
  • Modelisation and Computation

Eight specialisations
offered in the second year of study

  • Vehicle Dynamics and Intelligent Transport Systems
  • Internal Combustion Engines
  • Powertrains
  • Engines and Fuels

Multibody Modelling for Vehicle Systems

Type Compulsory
Semester winter
Contact hours 52 (3+1)
Number of credits 5
Type of termination Assessment + Exam
Form Lectures + exercises
Lecturers Prof. Dr. Ing. Michael Valášek
Prof. Dr. Ing. Zbyněk Šika  

Educate the basics of modeling of vehicle systems as multibody systems


  1. Development Process of Simulation Model
    Ideal objects of engineering sciences. Conceptual model, physical model, simulation model
  2. Matrix Formulation of Kinematics
    Matrix of directional cosines, transformation, velocity and acceleration matrices. Basic motions, basic transformation matrices. Method of basic matrices
  3. Different Coordinates for Description of Multibody Systems
    Independent and dependent, relative, Cartesian and physical coordinates. Euler angles, Cardan angles, Euler parameters. Kinematical description of open kinematic chain
  4. Solution of Kinematical Loops
    Kinematical solution of kinematical loops by method of closed loop, method of disconnected loop, method of removed body, method of natural coordinates, method of compartments (physical coordinates)
  5. Numerical Methods for Solution of Multibody Kinematics
    Position, velocity and acceleration problems. Solution of over- and under-constrained system of linear and nonlinear algebraic equations. Special and singular cases of multibody systems
  6. Kinematical Synthesis of Multibody Systems
    Engineering design process, formulation of kinematical synthesis, solving procedures, optimization. Synthesis of vehicle suspensions
  7. Dynamics of Multibody Systems by Lagrange Equations of Mixed Type
    Lagrange equations of mixed type, assembly of particular expressions. Multibody dynamic formalism by physical coordinates. Interpretation of Lagrange multipliers. Force elements for vehicle modelling
  8. Numerical Methods of DAE Solution
    Numerical problems of solution of differential-algebraic equations (DAE). Solution in indepenedent and dependent coordinates, Baumgarte stabilization, coordinate partitioning, projection into independent coordinates
  9. Advanced formulation of equations of motion of multibody systems
    Equivalence of Newton-Euler and Lagrange equations. Equations of motion of small vibrations. Dynamics of flexible multibody systems.
  10. Practice of multibody modelling
    Multibody modelling for different multibody dynamic formalisms. Example of modelling in Simpack. Modelling of vehicle suspension, modelling of vehicle dynamics

Study materials

  1. Lecturing material and hand-outs
  2. Stejskal, V., Valasek, M.: Kinematics and Dynamics of Machinery, Marcel Dekker, New York 1996 (basis textbook)

Czech Technical University in Prague

Technicka 4
16607 Prague 6
Czech republic

Phone: +420 224 352 499
Fax: +420 224 352 500


ITB – Institut Teknologi Bandung
Faculty of Mechanical and Aerospace Engineering

Jl. Ganesa 10
40132 Bandung

Phone: +62-22-2504243
Fax: +62-22-2534099


TU Chemnitz
Technische Universität Chemnitz Fakultät für Maschinenbau

Reichenhainerstr. 70, A016
D-09126 Chemnitz
Deutschland (Germany)

Phone: +49 371 531 31079
Fax: +49 371 531 831079


HAN – Hogeschool van Arnhem en Nijmegen
Institut of Automotive Engineering and Management

Ruitenberglaan 29
NL-6802 CC Arnhem
The Netherlands

Phone: +31 (0)6 55 20 88 19
Phone: +31 (0)26 365 82 15


ENSTA Bretagne
Ecole Nationale Supérieure de Techniques Avancées Bretagne

2, rue Francois Verny
F-29806 Brest Cedex 9

Phone: +33 (0)2 98 34 89 11
Fax: +33 (0)2 98 34 88 00


CTU in Prague
Coordinator of MAE

Gabriela Achtenová

IT Bandung | Head of Mechanical
Design Research Group

Andi Isra Mahyuddin

TU Chemnitz
Coordinator of MAE

Diana Lohse

HAN in Arnhem
Masters program manager

Kea Bouwman

ENSTA Bretagne
Coordinator of MAE

Yann Marco