Multi-Body Kinematics and Dynamics with Lie Groups
- 1st Edition - November 22, 2017
- Latest edition
- Authors: Dominique Paul Chevallier, Jean Lerbet
- Language: English
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 prope… Read more
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Description
Description
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
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
Readership
Readership
Table of contents
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
Product details
Product details
- Edition: 1
- Latest edition
- Published: November 22, 2017
- Language: English
About the authors
About the authors
DC
Dominique Paul Chevallier
JL