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. |
Dentro del libro
Resultados 1-5 de 62
... ................................. 306 308 9.9 The Clebsch-Gordan Coefficients and Wigner 3jm Symbols..........................................309 9.10 Differential Operators for SO( 3 )............................................
... coefficient. For the moment we will consider only functions of the form in Eq. (2.3). We shall see later in this section the conditions under which this expansion holds. A function f(x) e £ 2([0, L]) for which f( k )= 0 for all |£| > B ...
... coefficients, /(n), can be calculated by multiplying both sides of Eq. (2.3) by e~27nnx/L and integrating x over the ... coefficients Some authors prefer the choice of C — L to make the Fourier coefficients look neater. Others ...
... coefficients of 8(x) do not diminish as k increases, and so this Fourier series does not converge. This reflects the fact that <$(*) is not a “nice” function [i.e., it is not in £ 2([0, L])]. It is, nevertheless, convenient to view ...
... coefficients of the function f(x — Jto) can be calculated from those of /( jc) by making a change of variables y = x ... coefficients of df/dx, assuming / is at least a once differentiable function. Or, simply taking the derivative ...
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 |