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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... write G=R. The precise meaning of this equivalence will be given in Chapter 7. We now examine a generalization of this concept which will be extremely useful later in the book. Consider, instead of points on the line and translations ...
... write diffusion - type partial differential equations which evolve on the group of rigid - body motions . Noncommutative harmonic analysis serves as a tool for converting such equations into a domain where they can be solved efficiently ...
... write <$6(jc) = h€(x) for 0 < € << 1. Since it is always possible to choose € small enough that for any given v € R+, for engineering purposes f(x). 2Other “special” functions such as the Heaviside (unit) step function [17] defined as u ...
... write ( 2.11 ) This formula is critical in proving the inversion formula in general, and it is often called a completeness relation because it proves that the functions el0)X for all coe R are complete in £ 2(R) [i.e., any function in ...
... writes u(a>, t). Applying the Fourier transform to both sides of Eq. (2.20), and the initial conditions, one ... write ( 2.21 ) 2.3.2 The Schrodinger Equation In quantum mechanics, the Schrodinger equation for a free particle ...
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 |