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Syllabus for

Academic year
MMF131 - Applied systems dynamics
Owner: AUMAS
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 42 - APPLIED MECHANICS

Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0198 Examination 5,0 c Grading: TH   5,0 c   02 Jun 2007 pm V,  29 Aug 2007 pm V

In programs

TMASA MECHANICAL ENGINEERING - Automotive Engineering, Year 4 (elective)


Professor  Viktor Berbyuk


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Comprehensive knowledge of rigid body dynamics.


TThe course aims to introduce a powerful multibody dynamics methods and computer based tools and provide hands on experience to use them for kinematic and dynamic analysis and design of advanced mechanical and structural systems. These methods and tools came to a broader use in the nineties and are currently in extensive use at aerospace, automotive, train and many others industries. The automotive industry seems to be the trendsetter for the fast development of these new tools. The computer tools which will be used in the course are commercial software packages MSC.ADAMS and MATLAB/Simulink that assemble and solve the non-linear differential equations of motion for mechanical systems. The solution obtained supplies information on motion and internal forces as response to applied external forces and/or prescribed partial motion of the system. The present course aims also to outline, how the equations of motion could be systematically derived and assembled and how these equations could be numerically solved. Such knowledge is helpful when working with multibody dynamics formalism based modern computer tools and at the same time the knowledge would enable the development of dedicated stand-alone procedures for the study of special (smaller) systems. Thus, the course aims not only to develop skills in modeling real world machines, mechanisms and complex systems in terms of rigid bodies, different joints and constraints and in solving dynamical problems by using commercial software MSC.ADAMS and MATLAB/Simulink, but also to provide knowledge to study simple systems from scratch.


The course has two objectives: 1) to give the student knowledge about powerful multibody dynamics methods and an understanding of how these methods are used for various applications, and 2) to make the student able to use efficiently software ADAMS and MATLAB/Simulink for kinematic and dynamic analysis and design of broad classes of mechanical systems.


The main emphasis is on general systems performing non-linear motion. Those systems are modeled in terms of rigid bodies, massless connectors (springs, dampers, wheel-road contact, ...) and idealized massless motion constraints (joints, hinges, ...) which is adequate, e. g., when studying piston motion in engines and vehicle motion when traveling over bumpy roads. Such systems are described by a combination of ordinary differential and algebraic equations, DAE, which form the core of high-end software (ADAMS, DADS, ...). MSC.ADAMS and MATLAB/Simulink will be used for training hands on skills. At the theoretical description of multibody systems special attention is called to the description of orientation of rigid bodies, which - opposite of the position - regular geometric vectors cannot describe. Instead, Euler angles (or similar) or Euler parameters have to be used. Further, the relationship between general force and velocity transformations is emphasized, leading to the concept of Lagrange multipliers, representing constraint forces. Also, the general relationship between system position/orientation and system velocity is observed, as the Jacobian matrix describes it. Using those tools and the Newton-Euler equations for rigid body motion, a recipe is given for the general derivation of equations of motion of any multibody system. Methods for numerical solution of DAE are reviewed. The learning phase is concentrated on learning theory and on solving assigned comprehensive and realistic problems.
For more information, see course home page:


There will be scheduled lectures for theory, problems solving sessions, and instructors assisted software training sessions. The learning phase is much concentrated on solving assigned comprehensive and realistic problems by using software ADAMS and MATLAB/Simulink.


Intermediate Dynamics by Edward J. Haug, Prentice-Hall Inc., 1992, ISBN 0-13-478926-1. MSC.ADAMS and MATLAB/Simulink Software manuals (Helps, Getting Started Using ADAMS/View and other). Applied Systems Dynamics, Lecture Notes by Viktor Berbyuk, CHALMERS, 2006.


The final exam will be written. Completed MSC.ADAMS & MATLAB/Simulink Assigned Problems will be a pre-requisite for the exam.

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