(Created 2009-08-11.)

MULTIBODY DYNAMICS | FMEN01 |

**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.