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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: A
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   30 May 2006 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.


The course aims to introduce a powerful analytical computer based tool and provide hands on experience to use it at the study of the dynamics of discrete mechanical systems. This tool came to a broader use in the nineties and is currently in extensive use at many industries. The automotive industry seems to be the trendsetter for the fast development of that new tool. The tool is some commercial software package that assembles and solves the non-linear ordinary differential equations of motion for discrete mechanical systems. The solution, obtained by integration, supplies information on motion and internal forces as response to applied external forces and/or prescribed partial motion.
The present course aims also to outline, how the equations of motion could be systematically derived and assembled and how those equations could be numerically solved. Such 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 and mechanisms in terms of rigid bodies and massless connectors & constraints and in solving dynamical problems by using commercial software, but also to provide knowledge to study simple systems from scratch.


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, ...). One of those packages, ADAMS, will be used for training hands on skills, especially emphasizing pre-modeled generic vehicles (e. g., ADAMS Car).
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 transfor-mations 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 discrete mechanical 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.


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 ADAMS.


Intermediate Dynamics by Edward J. Haug, Prentice-Hall Inc., 1992, ISBN 0-13-478926-1. Software manuals: Getting Started Using ADAMS/View , "Gettig Started Using ADAMS/Driveline", and Getting Started Using ADAMS/Car .


The final exam will be written. Completed assigned problems will be a pre-requisite for the exam.

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