The Theory of the Top. Volume I (eBook)

Introduction to the Kinematics and Kinetics of the Top
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2008 | 2008
XX, 280 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4721-6 (ISBN)

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The Theory of the Top. Volume I - Felix Klein, Arnold Sommerfeld
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The lecture series on the Theory of the Top was originally given as a dedication to Göttingen University by Felix Klein in 1895, but has since found broader appeal. The Theory of the Top: Volume I. Introduction to the Kinematics and Kinetics of the Top is the first of a series of four self-contained English translations that provide insights into kinetic theory and kinematics.


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 "e;idiosyncratic disposition,"e; 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 "e;almost no use was made of the theoretical framework developed atthebeginning"e;[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.

Contents 5
Preface 7
Translators’ Remarks 13
FOREWORD 14
Advertisement of the Book 16
Introduction to the Kinematics and Kinetics of the Top 18
The kinematics of the top 25
§ 1. Geometric treatment of the kinematics 25
§ 2. Analytic representation of rotations about a fixed point 33
§3. The meaning of the parameters a, ß, ., d 41
§4. The use of a, ß, ., d for the study of finite rotations 48
§ 5. Passage to the so- called infinitesimal rotations 57
§ 6. The example of regular precession 65
§ 7. Excursus on the theory of quaternions 73
Introduction to kinetics (statics and impulse theory) 87
§ 1. Contrast between continuously acting forces and impact forces the impulse for a single free mass particle
§ 2. The elementary statics of rigid bodies 99
§ 3. The concept of the impulse for the generalized top. Relation between the impulse vector and the rotation vector. Connection to the expression for the vis viva 111
§ 4. Transference of the preceding results to the special case of the symmetric top 122
§ 5. The two fundamental theorems on the behavior of the impulse vector in the course of the motion 128
§ 6. The theorem of the vis viva 133
§ 7. Geometric treatment of force- free motion of the top 138
§ 8. Rotation of the top about a permanent turning axis and the so- called stability of the rotation axis of a rapidly rotating top 146
The Euler equations, with further development of the kinetics of the top 156
§ 1. Derivation of the Euler equations 156
§ 2. Analytic treatment of the force- free motion of the top 165
§ 3. On the meaning of the Euler equations and their relation to the equations of Lagrange 172
§ 4. Guidance of the top on a prescribed path. D’Alembert’s principle 180
§ 5. Special development for the spherical top. Decomposition of the total resistance into an acceleration resistance and a deviation resistance 187
§ 6. The deviation resistance for regular precession of the symmetric top 192
§ 7. A new derivation of the deviation resistance for regular precession of the symmetric top. The Coriolis force 198
§ 8. Experimental demonstration of the deviation resistance. The top with one and two degrees of freedom 208
Addenda and Supplements 215
Translators’ Notes. 225
References 281
Index 293

Erscheint lt. Verlag 16.12.2008
Übersetzer Raymond J. Nagem, Guido Sandri
Zusatzinfo XX, 280 p. 43 illus.
Verlagsort Boston
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Geschichte der Mathematik
Naturwissenschaften Physik / Astronomie
Technik
Schlagworte 19th century • gyroscopic motion • Kinematics • quaterion theory • Rigid Bodies • rigid body • Rotation • spinning tops
ISBN-10 0-8176-4721-X / 081764721X
ISBN-13 978-0-8176-4721-6 / 9780817647216
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