Multi-Body Kinematics and Dynamics with Lie Groups (eBook)

Dominique Paul Chevallier, Jean Lerbet (Autoren)

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2017 | 1. Auflage
334 Seiten
Elsevier Science (Verlag)
978-0-08-102357-0 (ISBN)

Infos

Multi-body Kinematics and Dynamics with Lie Groups starts with an overview of the practical aspects of Lie groups based on the example of rotation groups and the Euclidean group which may be used in problems of kinematics and dynamics of rigid bodies. The book includes exercises allowing the reader to get familiar with this mathematical framework. For the more experienced readers, theoretical results that have appeared in some scientific articles are also included. For example, a complete classification of singularities of mechanisms is developed through exercises.

• 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

Dominique Paul Chevallier is a research director at the Institute Navier-ENPC since 2006. He obtained his PhD in 1973.

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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. 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

Produkt-Details

• Erscheint lt. Verlag: 1.12.2017
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-102357-X / 008102357X
• ISBN-13: 978-0-08-102357-0 / 9780081023570