Rigid Body Kinematics and C++ Code

Sergio Pissanetzky0-9762775-1-4

A modern, in-depth presentation of the theory and principles of Rigid Body Kinematics at a College-level, with C++ source code.

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Table of contents :
Introductory Remarks……Page 11
Instructions……Page 14
Acknowledgments……Page 15
Part I. Theory……Page 17
Symmetric and Positive Definite Matrices……Page 19
Diagonally Dominant Matrices……Page 21
Orthogonal Matrices……Page 22
Diagonal Matrices……Page 23
3 X 3 Skew-Symmetric Matrices……Page 24
The Orientation Matrix……Page 26
Rotating a Vector Around an Axis……Page 28
Orientation Matrix for a Rotated Coordinate System……Page 30
Introduction……Page 33
Basic Notions of Graph Theory……Page 34
Breadth-first Search and Adjacency Level Structures……Page 37
The Coordinate System Graph……Page 39
Coordinate Transformations……Page 41
Interpolating Orientations……Page 43
Spherical Coordinates and Direction……Page 44
The Bodies and Constraints Graph……Page 45
Tensors and Form Invariance of the Laws of Physics……Page 47
The Kinematic State and the State Variables……Page 48
Position and Velocity……Page 49
Differentiating the Orientation Matrix……Page 50
Angular Velocity……Page 52
Specific Coordinates……Page 55
Specific Coordinates and State Variables……Page 56
Specific Coordinates and the Equations of Motion……Page 58
Specific Coordinates and Constraints……Page 62
The Rigid Body Model……Page 65
Addition of Kinematic States……Page 67
Direct Subtraction of Kinematic States……Page 69
Transposed Subtraction of Kinematic States……Page 70
Inversion of Kinematic States……Page 71
Conventions……Page 73
The ZXZ Convention……Page 74
The ZYX Convention……Page 77
Euler Parameters……Page 80
Orientation Matrix……Page 81
Angular Velocity……Page 82
Axial Rotator……Page 84
Angular Velocity……Page 85
Implementation……Page 86
Part II. Code Documentation……Page 87
C++ Code for Rigid Body Kinematics……Page 89
All Families……Page 90
All Classes……Page 91
Family of Classes: Specific Coordinates……Page 93
Class AxialRotator……Page 94
AxialRotator Constructor Detail……Page 97
AxialRotator Method Detail……Page 98
Class EulerAngles……Page 106
EulerAngles Attribute Detail……Page 108
EulerAngles Constructor Detail……Page 109
EulerAngles Method Detail……Page 110
Class EulerAnglesZXZ……Page 118
EulerAnglesZXZ Constructor Detail……Page 120
EulerAnglesZXZ Method Detail……Page 122
Class EulerAnglesZYX……Page 129
EulerAnglesZYX Constructor Detail……Page 131
EulerAnglesZYX Method Detail……Page 133
Class EulerParams……Page 140
EulerParams Method Detail……Page 143
Class Orientator……Page 153
Orientator Constructor Detail……Page 156
Orientator Method Detail……Page 157
Class Translator……Page 166
Translator Constructor Detail……Page 168
Translator Method Detail……Page 169
Class TranslatorXYZ……Page 172
TranslatorXYZ Method Detail……Page 173
Class OrthoMatrix……Page 175
OrthoMatrix Constructor Detail……Page 179
OrthoMatrix Method Detail……Page 182
All Graphs Classes……Page 195
Class BCComponent……Page 196
BCComponent Constructor Detail……Page 197
Class BCEdge……Page 198
BCEdge Attribute Detail……Page 199
BCEdge Method Detail……Page 200
Class BCGraph……Page 202
BCGraph Constructor Detail……Page 204
BCGraph Method Detail……Page 205
Class BCVertex……Page 207
BCVertex Constructor Detail……Page 208
BCVertex Method Detail……Page 209
Class CSEdge……Page 210
CSEdge Attribute Detail……Page 214
CSEdge Constructor Detail……Page 215
CSEdge Method Detail……Page 216
Class CSGraph……Page 227
CSGraph Attribute Detail……Page 228
CSGraph Method Detail……Page 229
Class CSState……Page 231
CSState Attribute Detail……Page 235
CSState Method Detail……Page 236
Class CSVector……Page 250
CSVector Constructor Detail……Page 253
CSVector Method Detail……Page 255
Class CSVertex……Page 267
CSVertex Method Detail……Page 268
Class PComponent……Page 269
PComponent Attribute Detail……Page 271
PComponent Method Detail……Page 272
Class PComponentWithTree……Page 276
PComponentWithTree Attribute Detail……Page 279
PComponentWithTree Constructor Detail……Page 281
PComponentWithTree Method Detail……Page 282
Class PEdge……Page 287
PEdge Attribute Detail……Page 289
PEdge Constructor Detail……Page 290
PEdge Method Detail……Page 291
Class PGraph……Page 293
PGraph Attribute Detail……Page 296
PGraph Constructor Detail……Page 297
PGraph Method Detail……Page 298
Class PPath……Page 305
PPath Constructor Detail……Page 307
PPath Method Detail……Page 308
Class PPathClosed……Page 314
PPathClosed Method Detail……Page 316
Class PPathOpen……Page 320
PPathOpen Constructor Detail……Page 322
PPathOpen Method Detail……Page 323
Class PVertex……Page 329
PVertex Attribute Detail……Page 330
PVertex Constructor Detail……Page 331
PVertex Method Detail……Page 332
Class Body……Page 335
Body Attribute Detail……Page 340
Body Method Detail……Page 343
Class BodyManager……Page 353
BodyManager Constructor Detail……Page 355
BodyManager Method Detail……Page 356
Bibliography and Index……Page 361