The Theory of the Top. Volume I (eBook)
XX, 280 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4721-6 (ISBN)
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 |
| Haben Sie eine Frage zum Produkt? |
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