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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... written fiig ^1°g\) instead of fi(g\ og^"1). The answer is that in this particular example both are acceptable since g(x) og(y) = g(y) og(x), but in the generalizations to follow, this equality does not hold, and the definition in Eq ...
... Written as one expression, the original function is then (2.4) (2.5) It becomes obvious when written this way that there is freedom to insert an arbitrary cinstant C as follows In other words, we could have defined the Fourier series as ...
... written in the form (2.13) where C\ is an arbitrary constant (like C in the case of Fourier series) and C2 is a second arbitrary constant by which we can change the frequency variable: co = C200 . We have chosen C\ = C2 = 1. Other ...
... written in terms of the following cable properties (all per unit length): resistance, R, inductance, L, capacitance, C, and leakage, 5. Explicitly, It is straightforward to see that application of the Fourier transform yields for each ...
... written as (2.39) It then follows that the Fourier coefficients (quantities in parentheses) in Eq. (2.38) are equal to T • f( —nT) for each n e Z . Hence we can rewrite Eq. (2.39) as After changing the order of integration and summation ...
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 |