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Birkhäuser

The Theory of the Top. Volume I

Introduction to the Kinematics and Kinetics of the Top

  • Book
  • © 2008

Overview

Authors:
  1. Felix Klein

    1. Mathematisches Institut, Universität Göttingen, Göttingen, Germany

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  2. Arnold Sommerfeld

    1. Fak. Mathematik, Universität München, München, Germany

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  • Provides insights into kinematic theory
  • Discusses practical uses of applied theoretical mechanics
  • Incorporates both historical matter and recent advances
  • Includes supplementary material: sn.pub/extras

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Table of contents (3 chapters)

  1. Front Matter

    Pages 1-16
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  2. Introduction to the Kinematics and Kinetics of the Top

    1. Front Matter

      Pages 1-7
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    2. The kinematics of the top

      • Raymond J. Nagem, Guido Sandri
      Pages 1-62

    3. Introduction to kinetics (statics and impulse theory)

      • Raymond J. Nagem, Guido Sandri
      Pages 1-69

    4. The Euler equations with further development of the kinetics of the top

      • Raymond J. Nagem, Guido Sandri
      Pages 1-59

  3. Back Matter

    Pages 1-83
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Keywords

About this book

TheTheory of the Top attained its great fame from both its monum- tal scope and its outstanding authors. In the early twentieth century, Felix Klein was known as a mathematician of world fame; Arnold S- merfeld, Klein’s disciple, had acquired his reputation as a rising star of theoretical physics. By 1910, when the ?nal volume of this tr- tise was published, the names of Klein and Sommerfeld would signal to a student that a matter as complex as the top was presented in a most authoritative manner, from the perspective of both mathem- ics and physics. The work also stands out in other regards: by its sheer extent—four volumes comprising a total of almost a thousand pages—and by the time lag of about ?fteen years between inception and completion. Klein himself regarded the ?nal result as somewhat disjointed. Its “idiosyncratic disposition,” he re?ected in 1922, may be understood only by taking into account the historic circumstances at its inception in 1895; the developments between the ?rst and last parts derailed the project from its intended course, so that for the technical applications described in Volume IV “almost no use was made of the theoretical framework developed atthebeginning”[Klein 1922, p. 659]. Itseemsappropriate,therefore,torecallthehistoricalcircumstances under which this treatise was conceived and pursued. Felix Klein was not only a renowned mathematician, but also an entrepreneurial and ambitious university professor striving for a broader acknowledgment of mathematics as a cultural asset.

Reviews

"This book is a translation by Raymond J. Nagem and Guido Sandri of the German original [F. Klein and A. Sommerfeld, Über die Theorie des Kreisels. Heft I, Teubner, Leipzig, 1897; JFM 28.0658.04]. Various editions of this book, which presents fundamental results in the theory of the motion of the top, have appeared in German...This English translation is of great scientific interest and importance. The content and sequence of exposition of this book faithfully follow the original work...The translators' remarks are presented separately and are intended to ensure an accurate account of the historical development of the theory of the top. This translation is of a high scientific caliber and makes one look forward to the translation of the second volume by Nagem and Sandri."   —Mathematical Reviews

"It is very positive that, by producing the English edition of this book, a large group of contemporary scientists and especially mathematicians can admire and appreciate what a broad understanding mathematicians like Felix Klein, not only of their field but also of physics, had. Very interesting ample notes of the translators (about 50 pages), where also various motions are worked out, physically interpreted and excellently illustrated by numerous figures, and a nice preface by Michael Eckert make this volume even more interesting to read than the German original."   —Zentralblatt MATH

Authors and Affiliations

  • Mathematisches Institut, Universität Göttingen, Göttingen, Germany

    Felix Klein

  • Fak. Mathematik, Universität München, München, Germany

    Arnold Sommerfeld

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