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Visit the National Academies Press Online, the Authoritative Source Motion, Control, and Geometry: Proceedings of a Symposium Board on Mathematical Sciences, National Research Council ISBN: 0-309-59061-2, 80 pages, 8.5 x 11, (1997) This free PDF was downloaded from: http://www.nap.edu/catalog/5772.html Visit the National Academies Press online, the authoritative source for all books from the National Academy of Sciences, the National Academy of Engineering, the Institute of Medicine, and the National Research Council: • Download hundreds of free books in PDF • Read thousands of books online for free • Purchase printed books and PDF files • Explore our innovative research tools – try the Research Dashboard now • Sign up to be notified when new books are published Thank you for downloading this free PDF. 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Motion, Control, and Geometry: Proceedings of a Symposium http://www.nap.edu/catalog/5772.html i MOTION, CONTROL, AND GEOMETRY Proceedings of a Symposium Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council riginal paper book, not the from original typesetting breaks files. Page are true ned, andned,typographic some errors may have been accidentally inserted. Please National Academy Press Washington, D.C. 1997 About this This PDF newfile: representation digital of original work the has been recomposed from createdXML files the from o the line lengths, word breaks,to original; heading styles,typesetting-specific and other formatting, however, cannot be retai use the print version of this publication as the authoritative version for attribution. Copyright © National Academy of Sciences. All rights reserved. Motion, Control, and Geometry: Proceedings of a Symposium http://www.nap.edu/catalog/5772.html ii NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose mem- bers are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee con- sisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineer- ing programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. William A. Wulf is interim president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initia- tive, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of sci- ence and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. William A. Wulf are chairman and interim vice-chairman, respectively, of the National Research Council. The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the Board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the Board is designed to conduct studies for federal agencies and maintain liai- riginal paper book, not the from original typesetting breaks files. Page are true son with the mathematical sciences communities and academia, professional societies, and industry. ned, andned,typographic some errors may have been accidentally inserted. Please The Board on Mathematical Sciences is supported by core funding from the following federal agencies: Air Force Office of Scientific Research, Army Research Office, Department of Energy, National Science Foundation, National Security Agency, and Office of Naval Research. This activity was supported by core funding. Any opinions, findings, conclusions, or recommendations expressed in this publica- tion are those of the authors and do not necessarily reflect the view of the organizations or agencies that provided support for the Board. Copyright 1997 by the National Academy of Sciences. All rights reserved. International Standard Book Number 0-309-05785-X Additional copies of this report are available from: Board on Mathematical Sciences National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418 Printed in the United States of America Cover: Rolling your finger in a circular motion on a rolling sphere generates rotations. Drawing courtesy of Jerrold E. Marsden, California Institute of Technology. About this This PDF newfile: representation digital of original work the has been recomposed from createdXML files the from o the line lengths, word breaks,to original; heading styles,typesetting-specific and other formatting, however, cannot be retai use the print version of this publication as the authoritative version for attribution. Copyright © National Academy of Sciences. All rights reserved. Motion, Control, and Geometry: Proceedings of a Symposium http://www.nap.edu/catalog/5772.html iii BOARD ON MATHEMATICAL SCIENCES AVNER FRIEDMAN, University of Minnesota, Chair LOUIS AUSLANDER, City University of New York MARY ELLEN BOCK, Purdue University PETER E. CASTRO, Eastman Kodak Company FAN R.K. CHUNG, University of Pennsylvania R. DUNCAN LUCE, University of California, Irvine ROBERT MACPHERSON, Institute for Advanced Study SUSAN MONTGOMERY, University of Southern California GEORGE NEMHAUSER, Georgia Institute of Technology ANIL NERODE, Cornell University DIANNE P. O'LEARY, University of Maryland INGRAM OLKIN, Stanford University RONALD F. PEIERLS, Brookhaven National Laboratory DONALD ST. P. RICHARDS, University of Virginia WILLIAM P. ZIEMER, Indiana University riginal paper book, not the from original typesetting breaks files. Page are true Ex Officio Member ned, andned,typographic some errors may have been accidentally inserted. Please DARYL PREGIBON, Bell Laboratories Chair, Committee on Applied and Theoretical Statistics Staff JOHN R. TUCKER, Director RUTH E. O'BRIEN, Staff Associate BARBARA W. WRIGHT, Administrative Assistant About this This PDF newfile: representation digital of original work the has been recomposed from createdXML files the from o the line lengths, word breaks,to original; heading styles,typesetting-specific and other formatting, however, cannot be retai use the print version of this publication as the authoritative version for attribution. Copyright © National Academy of Sciences. All rights reserved. Motion, Control, and Geometry: Proceedings of a Symposium http://www.nap.edu/catalog/5772.html iv COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS ROBERT J. HERMANN, United Technologies Corporation, Co-chair W. CARL LINEBERGER, University of Colorado, Co-chair PETER M. BANKS, Environmental Research Institute of Michigan LAWRENCE D. BROWN, University of Pennsylvania RONALD G. DOUGLAS, Texas A&M University JOHN E. ESTES, University of California, Santa
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