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Multi-body kinematics and dynamics with Lie groups

Author: Dominique P Chevallier; Jean Lerbet
Publisher: London : ISTE Press Ltd ; Oxford : Elsevier Ltd, 2018.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Chevallier, Dominique P.
Multi-body kinematics and dynamics with lie groups.
London, England ; Oxford, England : ISTE Press ; Elsevier, ©2018
xviii, 317 pages
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Dominique P Chevallier; Jean Lerbet
ISBN: 9780081023570 008102357X
OCLC Number: 1013541227
Description: 1 online resource
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
Responsibility: Dominique P. Chevallier, Jean Lerbet.

Abstract:

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.

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