Dominique Paul ChevallierJean Lerbet - Multi-Body Kinematics and Dynamics with Lie Groups

Dominique P. Chevallier

Jean Lerbet

Series Editor

Nol Challamel

First published 2018 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd

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ISBN 978-1-78548-231-1

Printed and bound in the UK and US

set of integers

ring of rational integers

real number field

real quaternion field (Appendix 1 to )

dual number ring (see )

dual number such that 2 = 0 (see )

Df differential of the map f (see )

f T tangent map of the map f (see )

symbol of the composition of maps

Euclidean affine space (generally of dimension 3)

Tr ( u ) translation in by the vector uE (see )

E vector space (very often the Euclidean of dimension 3 over )

vector product (or cross product) in the oriented dimension 3 Euclidean vector space

mapping x a x in the oriented dimension 3 Euclidean vector space

[ | ] Lie bracket in a Lie algebra

(; ; ) mixed product in the dimension 3 Euclidean vector space

{ | } dual mixed product in the -module D (see )

{; ; } dual mixed product in the -module D (see )

E algebra of the linear operators in the vector space E (see )

GlE group of the regular linear operators the vector space E (see )

OE Orthogonal group of the Euclidean vector space E (see )

SOE Special othogonal group of the Euclidean vector space E (see )

U group of the normalized quaternions

Ga group of affine transformations of

D,D Displacement group of

D,D Lie algebra of D (of the skewsymmetric vectorfields on see )

| Klein form of D (see )

set of vector fields DT vanishing on their axe (see )

a