The Theory of the Top. Volume IV: Technical Applications of the Theory of the Top

264 Pages·2014·3.993 MB·English

by  Felix Klein, Arnold Sommerfeld (auth.)

(cid:55)
Felix Klein
Arnold Sommerfeld
The Theory of the Top
Volume IV
Technical Applications of the
Theory of the Top
Translated by
Raymond J. Nagem
Guido Sandri

Felix Klein
Arnold Sommerfeld
The Theory of the Top
Volume IV
Technical Applications of the Theory of the Top
Raymond J. Nagem
Guido Sandri
Translators
Foreword to Volume IV by Michael Eckert
Translators:
Raymond J. Nagem Guido Sandri
Department of Mechanical Engineering Department of Mechanical Engineering
Boston University Boston University
Boston, MA, USA Boston, MA, USA

ISBN 978-0-8176-4826-8 ISBN 978-0-8176-4829-9 (eBook)
DOI 10.1007/978-0-8176-4829-9
Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2008926224

Mathematics Subject Classification (2010): 01A55, 01A75, 70E05, 70E50, 70E55, 70Q05

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Contents
Foreword ................................................. vii
Preface.................................................... xi
Advertisement. ............................................ xiii
Volume IV.
Technical Applications of the Theory of the Top.
Chapter IX.
Technical applications.
§1. The most important formula in the theory of the top.
Generalities on stabilization by the gyroscopic effect......... 761
§2. Gyroscopic effects in railway operation. ................... 771
§3. The torpedo guidance apparatus. The Whitehead and
Howell torpedoes. ...................................... 782
§4. The Schlick gyroscopic ship stabilizer.
Generalities and theory. ................................. 794
§5. Specialized discussion of the effect of the ship stabilizer...... 810
§6. Results and practical experience with the ship stabilizer. .... 833
§7. The gyroscopic compass. ................................ 845
§8. Stability of the bicycle. ................................. 863
§9. On alleged and actual gyroscopic effects
for the Laval turbine. ................................... 884
§10.Miscellaneous applications. .............................. 899
A. Single-rail trains. .................................... 900
1. The suspension railway. ............................ 900
2. The monorail system............................... 902
3. The system of Brennan and Scherl................... 903
v
vi Contents.
B. Nautical applications. ................................ 914
4. The paddle steamer................................ 914
5. The turbine steamer. .............................. 916
6. The gyroscopic horizon............................. 919
7. Remarks on aeronautics. ........................... 921
C. Ballistics............................................ 922
8. The dynamic-hydrodynamic problem................. 923
9. The general empirical facts of ballistics and the
role of gyroscopic effects............................ 928
Translators’ Notes. ......................................... 937
References................................................. 995
Index.................................................... 1005
vi
Foreword
Felix Klein recalled in 1922 that The Theory of the Top had originated
in lectures that were intended to be publishedas a pamphlet dedicated
to the Association for the Advancement of Teaching in Mathematics
and the Sciences. “In the hands of my former assistant Sommerfeld,
however,” Klein wrote, “these lectures were turned into an extensive
book” [Klein 1922, p. 509]. The four volumes that were published in
1897, 1898, 1903, and 1910 bear witness to the extent of Sommerfeld’s
effort, and to the growing departure from Klein’s original plan. The
more the work considered applications, the less it made use of the
mathematical concepts (such as quaternions) introduced in the first
volume. Mathematical beauty receded in favor of the complexity in-
volved in addressing astronomical, geophysical, and technical matters.
The fourth volume appears almost as an antithesis of the first, with
only as much mathematical formalism as necessary in order to cope
with one or another technological application.
The time lag between the fourth volume and its predecessors also
illustrates the growing divergence from the initial plan. When Klein
asked Sommerfeld about the progress of the work in November 1904,
one year after the appearance of Volume III, Sommerfeld apologized
that he had not had time to think about the top, because he was then
busy with research in the theory of electrons. “But the top will still
be completed, and for the most part, I think, this winter,” he calmed
Klein’s impatience [Sommerfeld 1904]. Needless to add, this prediction
was too optimistic. “I no longer dare to remind you of it,” Klein wrote
to Sommerfeld again three years later [Klein 1907].
By this time, Sommerfeld was no longer professor at the Technische
Hochschule in Aachen, wherethe theory of the top had belonged to the
subjects of his own courses. In the summer of 1906, he had accepted a
vii
viii Foreword.
call to the University in Munich as professor of theoretical physics (for
Sommerfeld’s biography, see [Eckert 2013]). The technical applications
of the top intended for the fourth volume, such as the gyrocompass,
the stability of the bicycle, and gyroscopic effects in other practical de-
vices, were no longer part of his professorial duties, although he could
not resist including such topics in his later Munich lectures on me-
chanics [Sommerfeld 1952]. However, he had drafted several parts of
the manuscript for the fourth volume as early as 1900, when he was
called to Aachen, and, in view of a widespread distrust at the Techni-
sche Hochschuleagainstmathematicians fromuniversities,waseagerto
comply with the expectations of engineers by choosing gyroscopic ap-
plications to ballistics and torpedoes as examples. Furthermore, there
wereothersonwhoseassistancehecouldrely,suchasKlein’sG¨ottingen
colleagues Karl Schwarzschild and Emil Wiechert for the astronomical
and geophysical applications in the third volume. For the fourth vol-
ume he could count in particular on Fritz Noether, the brother of the
famous mathematician Emmy Noether. Fritz Noether had attended
Sommerfeld’s lectures and considered himself his pupil, although he
obtained his doctoral degree in February 1909 in mathematics with
Aurel Voss as his thesis advisor and with theoretical physics only as a
subsidiary subject [Noether 1909]. In his preface to Volume IV, Som-
merfeld thanked Fritz Noether as “an independent collaborator with
expertise in mechanics.” Noether’s assistance was also acknowledged
on the title page.
Sommerfeld’s and Noether’s effort for The Theory of the Top did
not end with the publication of the fourth volume. One year after its
appearance, the publisher informed Sommerfeld that a new edition of
the first volume would soon be expedient. The First World War in-
terrupted the swift appearance of new editions, but by 1921 the first
three volumes were available in a new printing. There seems to have
been no such demand for the fourth volume, because the engineering
applications of the theory of the top were subject of a number of more
specialized treatises, but this did not reduce Sommerfeld’s reputation
asanexpertinthesematters. Hewasasked, forexample, forhisexpert
opinion in patent disputes on gyroscopic compasses [Broelmann 2002,
pp. 328–346]. One of his disciples, Karl Glitscher, became employed
in the gyrocompass firm of Hermann Anschu¨tz-Ka¨mpfe. In the First
World War, Sommerfeld and Noether made use of their expert knowl-
edge in a study of gyroscopic effects in ballistics (described in general
terms in the last section of this volume). Fritz Noether made a name
viii
Foreword. ix
for himself as an expert in many fields of applied mathematics. When
the Nazis came to power in 1933, he emigrated to the Soviet Union,
where he fell victim to Stalin’s purges [Schlote 1991]. In August 1940,
Sommerfeldasked theRussianAcademy forhelp,buthisappealwas to
no avail. A year later, Noether was sentenced to death and shot. In his
appeal to the Russian Academy, Sommerfeld mentioned that “Noether
has provided me with valuable help for the elaboration of the fourth
partofthetheoryofthetopeditedbyFelixKleinandmyself,”recalling
once more Noether’s part in this effort [Sommerfeld 1940].
The contributions of Schwarzschild, Wiechert, Noether, and others
remind us that voluminous works of this kind are seldom the result of
solitarycontemplation intheivorytowerofscience. Ifweconsidertheir
involvement, The Theory of the Topbecomesahistoricalmonumentfor
scientists andengineers whosecontributions areusuallyrememberedin
other areas or forgotten altogether. From the broader perspective of
the history of science, The Theory of the Top is much more than the
legacy of a legendary mathematician and a famous theoretical physi-
cist. Its genesis and the process of its realization demonstrate how
technology was regarded by its authors first and foremost as a means
for exposing the virtues of science. Although the fourth volume was
devoted explicitly to applications in technology, Klein and Sommerfeld
still hoped, as they wrote in their 1910 foreword, that the top would
prove worthy of the honorable name of a philosophical instrument.
Michael Eckert
Deutsches Museum, Munich
ix