Multi-Body Kinematics and Dynamics With Lie Groups by Dominique Paul Chevallier,Jean Lerbet -- Read -- Imperial Library of Trantor

Index

Cover Title page Table of Contents Copyright List of Notations Introduction 1: The Displacement Group as a Lie Group

Abstract 1.1 General points 1.2 The groups O(E) and SO(E) as Lie groups 1.3 The group U of normalized quaternions 1.4 Cayley transforms 1.5 The displacement group as a Lie group 1.6 Conclusion 1.7 Appendix 1: The algebra of quaternions 1.8 Appendix 2: Lie subalgebras and ideals of D

2: Dual Numbers and "Dual Vectors" in Kinematics

Abstract 2.1 The Euclidean module D over the dual number ring 2.2 Dualization of a real vector space 2.3 Dual quaternions 2.4 Differential calculus in Δ-modules

3: The “Transference Principle”

Abstract 3.1 On the meaning of a general algebraic transference principle 3.2 Isomorphy between the adjoint group D∗ and SO(Ê) 3.3 Regular maps 3.4 Extensions of the regular maps from U to SO(E)

4: Kinematics of a Rigid Body and Rigid Body Systems

Abstract 4.1 Introduction 4.2 Kinematics of a rigid body 4.3 The position space of a rigid body 4.4 Relations to the models of bodies 4.5 Changes of frame in kinematics 4.6 Graphs and systems subjected to constraints 4.7 Kinematics of chains

5: Kinematics of Open Chains, Singularities

6: Closed Kinematic Chains: Mechanisms Theory

Abstract 6.1 Geometric framework and regular case 6.2 Exhaustive classification of the local singularities of mechanisms 6.3 Singular mechanisms with degree of mobility one 6.4 Concrete examples and calculations

7: Dynamics

Abstract 7.1 Changes of frame in dynamics, objective magnitudes 7.2 The inertial mass of a rigid body 7.3 The fundamental law of dynamics

8: Dynamics of Rigid Body Systems

Bibliography Index