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Nonetheless, he is required by Hence, fewwith knowledge in this area have had access to the engineering problems that can be addressed usingthis area of mathematics. Secondly, without knowing of the existence of this powerful and beautifularea of mathematics, it has been impossible for engineers to formulate their problems within thisframework, and thus impossible to apply it. Thus this book can be viewed as a bridge of sorts.
On theone hand, mathematicians who are familiar with abstract formulations can look to this book and seegroup representation theory and harmonic analysis being applied to a number of problems of interestin engineering.
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Likewise, engineers completely unfamiliar with these concepts can look to this textto gain the vocabulary needed to express their problems in a new and potentially more efficient way. Chapter 1 is an overview of several engineering problems to which this theory is applicable.
InChapter 2 we review commutative harmonic analysis classical Fourier analysis and associatedcomputational issues that have become so important in all areas of modern engineering. Chapter 3is a review of the orthogonal expansions of classical mathematical physics combined with moremodern techniques such as Walsh functions, discrete polynomial transforms, and wavelets. Advancedengineering mathematics with emphasis on curvilinear coordinate systems and basic coordinate-dependent differential geometry of hyper-surfaces in RN is the subject of Chapter 4.
Chapters 5and 6 are each devoted to the properties and parameterizations of the two groups of most importancein the application areas covered here: the rotation group and the group of rigid-body motions. Forthe most part, we do not use group theoretical notation in Chapters 5 and 6.
In Chapter 7 we presentideas from group theory that are the most critical for the formulation in the remainder of the book.
This includes many geometrical examples of groups and cosets. The distinction between discrete andcontinuous groups is made, and the classification of continuous groups using matrix techniques is.
In Chapter 8 we discuss how to integrate functions on continuous Lie groups and presentthe general ideas of representation theory and harmonic analysis on finite and compact Lie groups. Chapter 9 is devoted to orthonormal expansions on the rotation group and related mathematicalobjects such as the unit sphere in four dimensions. In Chapter 10 we present the theory behindFourier analysis on the Euclidean motion groups groups of rigid-body motions in the plane andspace.
These are groups that we have found to be of great importance in engineering applications though they are rarely discussed in any detail in mathematics textbooks and research monographs.
Chapter 11 develops a fast Fourier transform for the motion groups. Chapters are devotedexclusively to concrete applications of noncommutative harmonic analysis in engineering and appliedscience. A chapter is devoted to each application area: robotics; image analysis and tomography; posedetermination and sensor calibration; estimation and control with emphasis on spacecraft attitude;rotational Brownian motion and diffusion including the analysis of liquid crystals ; conformationalstatistics of macromolecules; and orientational averaging in mechanics.
This book can serve as a supplement for engineering, applied science, and mathematics studentsat the beginning of their graduate careers, as well as a reference book for researchers in any fieldof engineering, applied science, or mathematics. Clearly there is too much material for this bookto be used as a 1year course. However, there are many ways to use parts of this book as referencematerial for semester-long or quarter-long courses.
Engineering - Mechanical
We list several options below:. Writing a book such as this requires the efforts and input of many people. We would like to thanka number of people for their helpful comments and discussions which have been incorporated intothis text in one way or another. Special thanks goes to Imme Ebert-Uphoff, whose initial work under the supervision of the firstauthor led us to study noncommutative harmonic analysis, and to David Stein for preparing manyof the figures in this book.
We also acknowledge the support of the NSF, without which this workwould not have been pursued. Post on Dec views. Category: Documents 12 download. ChirikjianAlexander B. CRC Press This book contains information obtained from authentic and highly regarded sources.
Harmonic analysis - Wikipedia
Corporate Blvd. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only foridentification and explanation, without intent to infringe. Chirikjian, Alexander B. Kyatkin, Alexander B.