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 83
... Examples...................................................................................... Permutations and M ... Examples of Definitions: Symmetry Operations on the Equilateral Triangle (Revisited) ...
... example, to an engineer working on a particular application, there may be no difference between the unit step function shown in Fig. 1.4 with solid lines [which is not continuous, rapidly decreasing, or even in £ P(R, dx)], and its ...
... 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. (1.3) remains a useful definition in applications. Denoting the real numbers as R ...
... example , the extent to which rubber will stretch can be explained with knowledge of the end - to - end probability density function . In the context of DNA , a vast body of literature exists which addresses the probability that a ...
... example, [20]). 2.5. Discrete. and. Fast. Fourier. Transforms. Many physical phenomena are approximated well as being continuous, and the Fourier transform is a natural tool to model or aid in the analytical solution of equations describing ...
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 |
Otras ediciones - Ver todas
Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis ... Gregory S. Chirikjian,Alexander B. Kyatkin Sin vista previa disponible - 2021 |