Elements of Quaternions

Arthur Sherburne Hardy

Ginn, Heath, & Company, 1881 - 230 σελίδες

Περιεχόμενα

• Addition and Subtraction of Vectors or Geometric: 1
• Definition of a scalar: 8
• Complanar vectors: 15
• Analytical expression for a quaternion Product and quo: 24
• Expression for a medial vector: 25
• Negative sign commutative with i j: 30
• CHAPTER II: 32
• Distributive law true of the products of i j: 36
• Products of two vectors: 56
• Relation between the vector and Cartesian determination: 64
• Reciprocal of a vector scalar and quaternion: 70
• Article Page 54 Applications: 82
• Addition and subtraction of quaternions K S and V dis: 84
• Formulae relating to the products of two or more vectors: 99
• Exercises: 106
• Examples Applications to Spherical Trigonometry: 112
• General Formulae: 119
• Applications to Plane Trigonometry: 125
• CHAPTER III: 131
• Use of Cartesian forms in conjunction with quaternion rea soning: 132
• Quaternion differentiation: 134
• Illustration: 136
• Distributive principle: 138
• Quadrinomial form: 139
• Examples: 140
• 68: 145
• Right line through two given points: 146
• Perpendicular to a given line its length: 147
• Equations of a right line are linear and involve one indepen dent variable scalar: 150
• The Plane 73 Equation of a plane: 151
• Multiplication of quaternions not commutative Unq пUq: 152
• Plane through three given points: 153
• Equations of a plane are linear and involve two independent variable scalars: 154
• The Circle and Sphere 78 Equations of the circle: 164
• Distributive and associative laws in quaternion and vector: 165
• Article Page 80 Tangent line and plane: 166
• Chords of contact: 167
• Exercises in the transformation and interpretation of ele mentary symbolic forms: 176
• The Conic Sections Cartesian Forms 84 The parabola: 178
• Examples on the parabola: 180
• Relations between three intersecting tangents to the para bola: 185
• The ellipse: 191
• Examples on the ellipse: 192
• The hyperbola: 195
• Linear equation in quaternions Conjugate and selfconju gate functions: 199
• General equations of the conic sections: 201
• The ellipse: 204
• Examples: 206
• The parabola: 214
• Examples: 216
• The cycloid: 222
• Elementary applications to mechanics: 223

Πληροφορίες βιβλιογραφίας

• Τίτλος: Elements of Quaternions
• Συγγραφέας: Arthur Sherburne Hardy
• Εκδότης: Ginn, Heath, & Company, 1881
• Πρωτότυπο από: το Πανεπιστήμιο του Μίτσιγκαν
• Ψηφιοποιήθηκε στις: 21 Ιουν. 2007
• Μέγεθος: 230 σελίδες