Klein / Sommerfeld The Theory of the Top. Volume I

Introduction to the Kinematics and Kinetics of the Top
1. Auflage 2008
ISBN: 978-0-8176-4721-6
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 280 Seiten

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.

Autoren/Hrsg.

Klein, Felix

Sommerfeld, Arnold

Weitere Mitwirkende

Nagem, Raymond J.

Sandri, Guido

Inhaltsverzeichnis

1;Contents;5
2;Preface;7
3;Translators’ Remarks;13
4;FOREWORD;14
5;Advertisement of the Book;16
6;Introduction to the Kinematics and Kinetics of the Top;18
6.1;The kinematics of the top;25
6.1.1;§ 1. Geometric treatment of the kinematics;25
6.1.2;§ 2. Analytic representation of rotations about a fixed point;33
6.1.3;§3. The meaning of the parameters a, ß, ., d;41
6.1.4;§4. The use of a, ß, ., d for the study of finite rotations;48
6.1.5;§ 5. Passage to the so- called infinitesimal rotations;57
6.1.6;§ 6. The example of regular precession;65
6.1.7;§ 7. Excursus on the theory of quaternions;73
6.2;Introduction to kinetics (statics and impulse theory);87
6.2.1;§ 1. Contrast between continuously acting forces and impact forces; the impulse for a single free mass particle;87
6.2.2;§ 2. The elementary statics of rigid bodies;99
6.2.3;§ 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
6.2.4;§ 4. Transference of the preceding results to the special case of the symmetric top;122
6.2.5;§ 5. The two fundamental theorems on the behavior of the impulse vector in the course of the motion;128
6.2.6;§ 6. The theorem of the vis viva;133
6.2.7;§ 7. Geometric treatment of force- free motion of the top;138
6.2.8;§ 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
6.3;The Euler equations, with further development of the kinetics of the top;156
6.3.1;§ 1. Derivation of the Euler equations;156
6.3.2;§ 2. Analytic treatment of the force- free motion of the top;165
6.3.3;§ 3. On the meaning of the Euler equations and their relation to the equations of Lagrange;172
6.3.4;§ 4. Guidance of the top on a prescribed path. D’Alembert’s principle;180
6.3.5;§ 5. Special development for the spherical top. Decomposition of the total resistance into an acceleration resistance and a deviation resistance;187
6.3.6;§ 6. The deviation resistance for regular precession of the symmetric top;192
6.3.7;§ 7. A new derivation of the deviation resistance for regular precession of the symmetric top. The Coriolis force;198
6.3.8;§ 8. Experimental demonstration of the deviation resistance. The top with one and two degrees of freedom;208
6.4;Addenda and Supplements;215
6.5;Translators’ Notes.;225
6.6;References;281
7;Index;293