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Multi-Body Kinematics and Dynamics with Lie Groups - 1st Edition - ISBN: 9781785482311, 9780081023570

Multi-Body Kinematics and Dynamics with Lie Groups

1st Edition

Authors: Dominique Chevallier Jean Lerbet
eBook ISBN: 9780081023570
Hardcover ISBN: 9781785482311
Imprint: ISTE Press - Elsevier
Published Date: 22nd November 2017
Page Count: 334
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Multi-body Kinematics and Dynamics with Lie Groups explores the use of Lie groups in the kinematics and dynamics of rigid body systems.

The first chapter reveals the formal properties of Lie groups on the examples of rotation and Euclidean displacement groups. Chapters 2 and 3 show the specific algebraic properties of the displacement group, explaining why dual numbers play a role in kinematics (in the so-called screw theory). Chapters 4 to 7 make use of those mathematical tools to expound the kinematics of rigid body systems and in particular the kinematics of open and closed kinematical chains. A complete classification of their singularities demonstrates the efficiency of the method.

Dynamics of multibody systems leads to very big computations. Chapter 8 shows how Lie groups make it possible to put them in the most compact possible form, useful for the design of software, and expands the example of tree-structured systems.

This book is accessible to all interested readers as no previous knowledge of the general theory is required.

Key Features

  • Presents a overview of the practical aspects of Lie groups based on the example of rotation groups and the Euclidean group
  • Makes it clear that the interface between Lie groups methods in mechanics and numerical calculations is very easy
  • Includes theoretical results that have appeared in scientific articles


Engineers and Scientists working with multibody systems (robotics, designers). Organizations such as ASME, ASCE, any university libraries

Table of Contents

1. The Displacement Group as a Lie Group
2. Dual Numbers and "Dual Vectors" in Kinematics
3. The "Transference Principle"
4. Kinematics of a Rigid Body and Rigid Body Systems
5. Kinematics of Open Chains, Singularities
6. Closed Kinematic Chains: Mechanisms Theory
7. Dynamics
8. Dynamics of Rigid Body Systems


No. of pages:
© ISTE Press - Elsevier 2017
22nd November 2017
ISTE Press - Elsevier
eBook ISBN:
Hardcover ISBN:

About the Authors

Dominique Chevallier

Dominique P. Chevallier is Emeritus Research Director at Navier Laboratory, Ecole Nationale des Ponts et Chaussées in France. His research interests are the mathematical methods of mechanics.

Affiliations and Expertise

Ecole Nationale des Ponts et Chaussées, France

Jean Lerbet

Jean Lerbet is Professor at the Universities of Evry and Paris Saclay in France. His research interests include differential geometry and mechanics, and stability.

Affiliations and Expertise

Universities of Evry and Paris Saclay, France

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