(Created 2010-07-25.)
 MULTIBODY DYNAMICS FMEN01
Credits: 8. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course might be given in English. FMEN01 overlaps following cours/es: FME071 and FME120. Optional for: F4, F4bem, F4tf, I4, M4bem. Course coordinator: Associate Prof. Per Lidström, per.lidstrom@mek.lth.se, Mechanics. Prerequisites: Basic courses in Mechanics, Linear Algebra and Calculus. Assessment: Hand in exercises and written exam. Further information: The course might be offered in English. Home page: http://www.mek.lth.se.

Aim
The aim of the course is to:

• provide knowledge of the basic theory of the dynamics of multibody systems consisting of rigid bodies as well as simple flexible bodies.

• give insight in the numerical analysis of the equations of multibody dynamics.

Knowledge and understanding
For a passing grade the student must

• be able to give an account of the most important results in the theory of multibody dynamics.

• be able to formulate theoretical models for systems of connected rigid bodies and simple elastic bodies.

• have knowledge of the commercial computer programmes that are available.

Skills and abilities
For a passing grade the student must

• be able to analyse certain simple multibody systems with the aid of computer programmes (Mathcad, FEM, MBS-programmes).

• be able to perform an analysis of a multi-body system and to present the results in a well-written report.

• be able to describe some technical problems in industrial applications that can be studied with multibody dynamics.

Judgement and approach
For a passing grade the student must

• be able to evaluate achieved results based on the problem formulation at hand as well as physical limitations.

Contents
Rigid body kinematics and dynamics; Euler angles,etc, inertia tensor, Euler equations, Energy and Effect. Fixed-axis rotation; reaction forces, dynamic balancing, stability, Gyroscopic movement.d'Alemberts principle. Lagranges equations; constraints, degrees of freedom, Lagrange function, generalized forces.Multibody systems; holonomic and non-holonomic constraints,contact forces, friction, loss of effect. Lagranges equations with constraints. Rigid and flexible bodies in systems;discretization and coordinate representation mass- and stiffness-matrices. Equations of motion, construction and numerical treatment.Computer programmes; ADAMS, Matlab.

Literature
Lidström P., Nilsson K.:Lecture Notes on Fundamentals of MultiBody Dynamics. Division of Mechanics, LTH, 2006.
A.A. Shabana: Dynamics of MultiBody Systems. 3rd Edition. Cambridge University Press.2005.