Preface

Numerical Analysis is an interdisciplinary topic which develops its strength only when viewed in close connection with applications.
Nowadays, mechanical engineers having computer simulation as a daily engineering tool must learn more and more techniques from that field. Mathematicians, on the other hand, are increasingly confronted with the need of developing special purpose methods and codes. This requires a broad interdisciplinary understanding and a sense for model-method interactions. With this monograph we give an introduction to selected topics of Numerical Analysis based on these facts. We dedicate our presentations to a very interesting discipline in computational engineering: multibody dynamics. Though the basic ideas and methods apply to other engineering fields too, we emphasize on having one homogeneous class of applications.
Both authors worked through many years in developing teams of different multibody codes. Interdisciplinary work also includes transferring ideas from one field to the other and a big amount of teaching - and that was the idea of this book.

This book is intended for students of mathematics, engineering and computer science, as well as for people already concerned with the solution of related topics in university and industry.

After a short introduction to multibody systems and the mathematical formulation of the equations of motion, the different numerical methods used to solve simulation tasks are presented. The presentation is supported by a simple model of a truck. This truck model will follow the reader from the title page to the appendix in various versions, specially adapted to the topics.
The models used in this book are not intended to be real-life models. They are constructed to demonstrate typical effects and properties occurring in practical simulations. The methods presented include linear algebra methods (linearization, stability analysis of the linear system, constrained linear systems, computation of nominal interaction forces), nonlinear methods (Newton and continuation methods for the computation of equilibrium states), simulation methods (solution of discontinuous ordinary differential and differential algebraic equations) and solution methods for inverse problems (parameter identification). Whenever possible, a more general presentation of the methods is followed by a special view, taking the structure of multibody equations into consideration.

Each chapter is divided into sections. Some of the material can be skipped during a first reading. An asterisk (*) in the section title is indicating these parts.

Nearly all methods and examples are computed using MATLAB programs and nearly all examples are related to the truck model. Those MATLAB programs which describe the truck itself are given in the appendix for supporting the description of the model. Others are given as fragments in the text, where MATLAB is used only as a piece of meta language to describe an algorithm. Some of the examples had been used in universitary and post universitary courses. These can be obtained among other information related to this book via the book's homepage.

We want to thank everyone who has helped us to write this book: our teachers, colleagues, friends and families.

November 1997 Edda Eich-Soellner and Claus Führer