Grassmann Algebra

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ExploringScrew<strong>Algebra</strong>.nb 9 7.6 Computing with Screws To be completed 2001 4 5
8 Exploring Mechanics 8.1 Introduction 8.2 Force Representing force Systems of forces Equilibrium Force in a metric 3-plane 8.3 Momentum The velocity of a particle Representing momentum The momentum of a system of particles The momentum of a system of bodies Linear momentum and the mass centre Momentum in a metric 3-plane 8.4 Newton's Law Rate of change of momentum Newton's second law 8.5 The Angular Velocity of a Rigid Body To be completed. 8.6 The Momentum of a Rigid Body To be completed. 8.7 The Velocity of a Rigid Body To be completed. 8.8 The Complementary Velocity of a Rigid Body To be completed. 8.9 The Infinitesimal Displacement of a Rigid Body To be completed. 8.10 Work, Power and Kinetic Energy To be completed. 2001 4 5
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Grassmann Algebra Exploring applica
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TableOfContents.nb 2 1.7 Exploring
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TableOfContents.nb 4 3.5 The Common
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TableOfContents.nb 6 5.2 Axioms for
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TableOfContents.nb 8 6.7 The Induce
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TableOfContents.nb 10 9 Exploring G
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Preface The origins of this book Th
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Preface.nb 3 Chapters 7 to 13: Expl
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1. Introduction 1.1 Background The
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Introduction.nb 3 the scientific wo
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Introduction.nb 5 A plane can be re
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Introduction.nb 7 We see here also
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Introduction.nb 9 �a�Α m �
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Introduction.nb 11 ¥ Scalars facto
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Introduction.nb 13 Here Det[x,y,v]
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Introduction.nb 15 Lines and planes
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Introduction.nb 17 Graphic showing
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Introduction.nb 19 x � ae1 � be
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Introduction.nb 21 Calculating inte
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Introduction.nb 23 1.11 Exploring H
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TheExteriorProduct.nb 2 � Calcula
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TheExteriorProduct.nb 4 This may be
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TheExteriorProduct.nb 6 At any stag
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TheExteriorProduct.nb 8 Note that w
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TheExteriorProduct.nb 10 � �1:
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TheExteriorProduct.nb 12 Grassmann
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TheExteriorProduct.nb 14 when gener
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TheExteriorProduct.nb 16 � Genera
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TheExteriorProduct.nb 18 BasisTable
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TheExteriorProduct.nb 20 That is: e
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TheExteriorProduct.nb 22 CobasisPal
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TheExteriorProduct.nb 24 � 1 The
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TheExteriorProduct.nb 26 ��
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TheExteriorProduct.nb 28 Let ei m b
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TheExteriorProduct.nb 30 Α1 � Α
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TheExteriorProduct.nb 32 2.9 Soluti
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TheExteriorProduct.nb 34 Evaluating
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TheExteriorProduct.nb 36 ��Α 2
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TheExteriorProduct.nb 38 Division b
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TheRegressiveProduct.nb 2 3.9 Produ
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TheRegressiveProduct.nb 4 The grade
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TheRegressiveProduct.nb 6 � �8:
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TheRegressiveProduct.nb 8 The inver
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TheRegressiveProduct.nb 10 1. Repla
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TheRegressiveProduct.nb 12 Example
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TheRegressiveProduct.nb 14 Here we
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TheRegressiveProduct.nb 16 Extendin
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TheRegressiveProduct.nb 18 Finally,
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TheRegressiveProduct.nb 20 Example:
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TheRegressiveProduct.nb 22 � Auto
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TheRegressiveProduct.nb 24 Y � Cr
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TheRegressiveProduct.nb 26 e1 �
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TheRegressiveProduct.nb 28 Similarl
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TheRegressiveProduct.nb 30 A 3 �
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TheRegressiveProduct.nb 32 Provided
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TheRegressiveProduct.nb 34 n � i
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TheRegressiveProduct.nb 36 � A 2-
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TheRegressiveProduct.nb 38 SimpleQ
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TheRegressiveProduct.nb 40 �Α m
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TheRegressiveProduct.nb 42 x p �
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TheRegressiveProduct.nb 44 Here the
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4 Geometric Interpretations 4.1 Int
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GeometricInterpretations.nb 3 and t
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GeometricInterpretations.nb 5 Sir W
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GeometricInterpretations.nb 7 A not
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GeometricInterpretations.nb 9 The g
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GeometricInterpretations.nb 11 simp
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GeometricInterpretations.nb 13 Deco
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GeometricInterpretations.nb 15 The
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GeometricInterpretations.nb 17 The
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GeometricInterpretations.nb 19 L
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GeometricInterpretations.nb 21 �P
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GeometricInterpretations.nb 23 �
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GeometricInterpretations.nb 27 Alte
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GeometricInterpretations.nb 29 �
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GeometricInterpretations.nb 33 P1
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TheComplement.nb 2 � Converting t
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TheComplement.nb 4 5.2 Axioms for t
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TheComplement.nb 6 essential underp
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TheComplement.nb 8 ��
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TheComplement.nb 10 Basis elements
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TheComplement.nb 12 ei m ��
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TheComplement.nb 14 Relating exteri
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TheComplement.nb 18 The default met
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TheComplement.nb 20 �3; DeclareMe
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TheComplement.nb 22 We can transfor
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TheComplement.nb 24 2 2 2 ��1,3
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TheComplement.nb 26 � Simplifying
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TheComplement.nb 28 ComplementTable
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TheComplement.nb 32 hence can be fa
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TheComplement.nb 38 ei m The comple
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TheComplement.nb 40 e i ��
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TheComplement.nb 42 Α m �Α1 �
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ExploringGrassmannAlgebra.nb 42 Gra
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10 Exploring the Generalized Grassm
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ExpTheGeneralizedProduct.nb 3 For b
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ExpTheGeneralizedProduct.nb 5 Α m
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ExpTheGeneralizedProduct.nb 11 Exam
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ExpTheGeneralizedProduct.nb 33 The
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ExpTheGeneralizedProduct.nb 35 Flat
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ExpTheGeneralizedProduct.nb 37 Prod
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11 Exploring Hypercomplex Algebra 1
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12 Exploring Clifford Algebra 12.1
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ExploringCliffordAlgebra.nb 3 12.17
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ExploringCliffordAlgebra.nb 33 Or,
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ExploringCliffordAlgebra.nb 41 scal
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ExploringCliffordAlgebra.nb 53 2001
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ExploringCliffordAlgebra.nb 55 numb
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ExplorGrassmannMatrixAlgebra.nb 2 1
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ExplorGrassmannMatrixAlgebra.nb 4 X
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ExplorGrassmannMatrixAlgebra.nb 8 A
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A Brief Biography of Grassmann Herm
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ABriefBiographyOfGrassmann.nb 3 I h
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Declarations �n �n declare a li
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Glossary To be completed. Ausdehnun
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Glossary.nb 3 Grade The grade of an
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Glossary.nb 5 Physical entities Poi
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Bibliography To be completed Armstr
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Bibliography2.nb 3 Clifford W K 187
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Bibliography2.nb 5 quaternions and
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Grassmann Algebra

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