Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion GroupsCRC Press, 2021 M02 25 - 674 páginas First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. |
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... points out that some imperfections in the original copies may be apparent . Disclaimer The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact . ISBN 13 ...
... ........ 135 137 138 141 5.7.1 Metrics on Rotations Viewed as Points in R4 ....................................................143 5.7.2 5.7.3 Metrics Resulting from Matrix Norm Geometry-Based M etrics............................
... points, and have convergent Taylor series), absolutely and square integrable, and rapidly decreasing. For functions defined on certain domains it is redundant to specify all of these conditions. For instance, a bounded function with ...
... points on the line and translations long the line, points in the plane and rigid motions in the plane. Any point in the plane can be described with matrices of the form and any rigid-body motion in the plane (translation and rotation) ...
... point source at x = 0 is given by We now may consider what happens to light from this point source as it passes through an opening, or aperture, in an otherwise opaque screen, as illustrated in Fig. 2.1. According to the Huygens ...
Contenido
| 1 | |
| 15 | |
| 39 | |
4 Orthogonal Expansions in Curvilinear Coordinates | 81 |
5 Rotations in Three Dimensions | 111 |
6 RigidBody Motion | 149 |
7 Group Theory | 187 |
8 Harmonic Analysis on Groups | 239 |
15 Stochastic Processes Estimation and Control | 485 |
16 Rotational Brownian Motion and Diffusion | 515 |
17 Statistical Mechanics of Macromolecules | 545 |
18 Mechanics and Texture Analysis | 579 |
A Computational Complexity Matrices and Polynomials | 607 |
B Set Theory | 615 |
C Vector Spaces and Algebras | 623 |
D Matrices | 627 |
9 Representation Theory and Operational Calculus for SU2 and SO3 | 281 |
10 Harmonic Analysis on the Euclidean Motion Groups | 321 |
11 Fast Fourier Transforms for Motion Groups | 353 |
12 Robotics | 379 |
13 Image Analysis and Tomography | 419 |
14 Statistical Pose Determination and Cam era Calibration | 455 |
E Techniques from Mathematical Physics | 635 |
F Variational Calculus | 645 |
G Manifolds and Riemannian Metrics | 651 |
References | 655 |
Index | 659 |
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Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis ... Gregory S. Chirikjian,Alexander B. Kyatkin Sin vista previa disponible - 2021 |