A Geometric Algebra Invitation To Space Time Physics Robotics And Molecular Geometry
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A Geometric Algebra Invitation To Space Time Physics Robotics And Molecular Geometry
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Author : Carlile Lavor
language : en
Publisher: Springer
Release Date : 2018-07-12
A Geometric Algebra Invitation To Space Time Physics Robotics And Molecular Geometry written by Carlile Lavor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Mathematics categories.
This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation; robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots; and molecular geometry, with 3D-protein structure calculations using NMR data. The book is primarily intended for graduate students and advanced undergraduates in related fields, but can also benefit professionals in search of a pedagogical presentation of these subjects.
Real Spinorial Groups
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Author : Sebastià Xambó-Descamps
language : en
Publisher: Springer
Release Date : 2018-11-22
Real Spinorial Groups written by Sebastià Xambó-Descamps and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with Mathematics categories.
This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
Systems Patterns And Data Engineering With Geometric Calculi
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Author : Sebastià Xambó-Descamps
language : en
Publisher: Springer Nature
Release Date : 2021-07-16
Systems Patterns And Data Engineering With Geometric Calculi written by Sebastià Xambó-Descamps and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-16 with Mathematics categories.
The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra. The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.
Sub Terahertz Sensing Technology For Biomedical Applications
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Author : Shiban Kishen Koul
language : en
Publisher: Springer Nature
Release Date : 2022-08-20
Sub Terahertz Sensing Technology For Biomedical Applications written by Shiban Kishen Koul and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-20 with Science categories.
This book offers the readers an opportunity to acquire the concepts of artificial intelligence (AI) enabled sub-THz systems for novel applications in the biomedical field. The readers will also be inspired to contextualize these applications for solving real life problems such as non-invasive glucose monitoring systems, cancer detection and dental imaging. The introductory section of this book focuses on existing technologies for radio frequency and infrared sensing in biomedical applications, and their limited use in sensing applications, as well as the advantages of using THz technology in this context. This is followed by a detailed comparative analysis of THz electronics technology and other conventional electro optic THz setups highlighting the superior efficiency, affordability and portability of electronics-based THz systems. The book also discusses electronic sub-THz measurement systems for different biomedical applications. The chapters elucidate two major applications where sub-THz provides an edge over existing state of the art techniques used for non-invasive measurement of blood glucose levels and intraoperative assessment of tumor margins. There is a detailed articulation of an application of leveraging machine learning for measurement systems for non-invasive glucose concentration measurement. This helps the reader relate to the output in a more user-friendly format and understand the possible use cases in a more lucid manner. The book is intended to help the reader learn how to build tissue phantoms and characterize them at sub-THz frequencies in order to test the measurement systems. Towards the end of the book, a brief introduction to system automation for biomedical imaging is provided as well for quick analysis of the data. The book will empower the reader to understand and appreciate the immense possibilities of using electronic THz systems in the biomedical field, creating gateways for fueling further research in this area.
Space Time Algebra
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Author : David Hestenes
language : en
Publisher:
Release Date : 1966
Space Time Algebra written by David Hestenes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Mathematical physics categories.
Geometric Algebra Applications Vol Ii
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Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer Nature
Release Date : 2020-06-19
Geometric Algebra Applications Vol Ii written by Eduardo Bayro-Corrochano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-19 with Mathematics categories.
This book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.
Applications Of Geometric Algebra In Computer Science And Engineering
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Author : Leo Dorst
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-03-08
Applications Of Geometric Algebra In Computer Science And Engineering written by Leo Dorst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-08 with Computers categories.
Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi-particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
Geometric Computing With Clifford Algebras
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Author : Gerald Sommer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Geometric Computing With Clifford Algebras written by Gerald Sommer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.
Geometric Fundamentals Of Robotics
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Author : J.M. Selig
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13
Geometric Fundamentals Of Robotics written by J.M. Selig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Technology & Engineering categories.
* Provides an elegant introduction to the geometric concepts that are important to applications in robotics * Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry * An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics
Geometric Algebra With Applications In Science And Engineering
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Author : Eduardo Bayro Corrochano
language : en
Publisher: Birkhäuser
Release Date : 2012-10-21
Geometric Algebra With Applications In Science And Engineering written by Eduardo Bayro Corrochano and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-21 with Mathematics categories.
The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.