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. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox. |
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... physics where he studied non - perturbative aspects of field theory . Currently he develops machine vision systems for industrial applications . He received a Ph.D. in physics from The Johns Hopkins University in 1996 . Preface This ...
... physics where he studied non - perturbative aspects of field theory . Currently he develops machine vision systems for industrial applications . He received a Ph.D. in physics from The Johns Hopkins University in 1996 . Preface This ...
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... physics. In contrast, we have made every attempt to make this book self-contained and readable for those with a standard background in engineering mathematics. Thus we present concepts in a heavily coordinate-dependent way without ...
... physics. In contrast, we have made every attempt to make this book self-contained and readable for those with a standard background in engineering mathematics. Thus we present concepts in a heavily coordinate-dependent way without ...
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... physics combined with more modern techniques such as Walsh functions , discrete polynomial transforms , and wavelets . Advanced engineering mathematics with emphasis on curvilinear coordinate systems and basic coordinate - dependent ...
... physics combined with more modern techniques such as Walsh functions , discrete polynomial transforms , and wavelets . Advanced engineering mathematics with emphasis on curvilinear coordinate systems and basic coordinate - dependent ...
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... Physics: Chapters 14, 16, 17. Writing a book such as this requires the efforts and input of many people. We would like to thank a number of people for their helpful comments and discussions which have been incorporated into this text in ...
... Physics: Chapters 14, 16, 17. Writing a book such as this requires the efforts and input of many people. We would like to thank a number of people for their helpful comments and discussions which have been incorporated into this text in ...
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Lo sentimos, el contenido de esta página está restringido..
Lo sentimos, el contenido de esta página está restringido..
Contenido
Preface | |
Classical Fourier Analysis | |
SturmLiouville Expansions Discrete Polynomial Transforms and Wavelets | xxvi |
Statistical Pose Determination and Camera Calibration | 14 |
Orthogonal Expansions in Curvilinear Coordinates | 21 |
The Möbius Band | 37 |
Rotations in Three Dimensions | 56 |
RigidBody Motion | 97 |
Image Analysis and Tomography | 241 |
Stochastic Processes Estimation and Control | 306 |
Rotational Brownian Motion and Diffusion | 333 |
Statistical Mechanics of Macromolecules | 66 |
Mechanics and Texture Analysis | 97 |
A Computational Complexity Matrices and Polynomials | 127 |
B Set Theory | 136 |
Vector Spaces and Algebras | 145 |
Group Theory | 121 |
Harmonic Analysis on Groups | 150 |
Representation Theory and Operational Calculus for SU2 and SO3 | 150 |
Harmonic Analysis on the Euclidean Motion Groups | 166 |
Fast Fourier Transforms for Motion Groups | 166 |
Robotics | 190 |
Matrices | 151 |
E Techniques from Mathematical Physics | 161 |
F Variational Calculus | 172 |
G Manifolds and Riemannian Metrics | 180 |
| 320 | |
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Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis ... Gregory S. Chirikjian,Alexander B. Kyatkin Sin vista previa disponible - 2021 |
Términos y frases comunes
A₁ algorithm analogous angular applications axis band-limited C₁ calculated Chapter Chirikjian class function coefficients computations conjugacy classes convolution coordinates corresponding cose coset d₁ defined definition denoted density function differential discrete motion group equation Euclidean group Euler angles example exponential f₁ finite groups follows Fourier series Fourier transform frame g₁ h₁ Hankel transform harmonic analysis Hence homogeneous transform homomorphism IEEE Trans inner product integration measure interpolation invariant inversion formula J₁ Jacobian kinematics Lie algebra Lie groups manipulator Math Mathematical matrix elements matrix exponential modules noncommutative notation operations orientation orthogonal orthonormal parameterized parameters Phys polynomials problem properties quaternions Radon transform rigid-body motions robot rotation matrix sample SE(D SE(N sine SO(D space sphere spherical subgroup symmetry theorem theory translation unitary representations V₁ values vector voxel wavelet transform workspace X₁