The Theory of the Top

by Klein, Felix; Sommerfeld, Arnold; Nagem, Raymond J.; Sandri, Guido; Eckert, Michael

• ISBN13: 9780817647209
• ISBN10: 0817647201
• Format: Hardcover
• Copyright: 2008-09-30
• Publisher: Birkhauser

Summary

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 of the classic and definitive treatment of rigid body motion.

Table of Contents

Preface	p. vii
Translators' Remarks	p. xiii
Foreword	p. xv
Advertisement	p. xvii
Introduction	p. 1
The kinematics of the top
Geometric treatment of the kinematics	p. 7
Analytic representation of rotations about a fixed point	p. 15
The meaning of the parameters [alpha], [beta], [gamma], [delta]	p. 23
The use of [alpha], [beta], [gamma], [delta] for the study of finite rotations	p. 30
Passage to the so-called infinitesimal rotations	p. 39
The example of regular precession	p. 47
Excursus on the theory of quaternions	p. 55
Introduction to kinetics (statics and impulse theory)
Contrast between continuously acting forces and impact forces; the impulse for a single free mass particle	p. 69
The elementary statics of rigid bodies	p. 81
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	p. 93
Transference of the preceding results to the special case of the symmetric top	p. 104
The two fundamental theorems on the behavior of the impulse vector in the course of the motion	p. 110
The theorem of the vis viva	p. 115
Geometric treatment of force-free motion of the top	p. 120
Rotation of the top about a permanent turning axis and the so-called stability of the rotation axis of a rapidly rotating top	p. 128
The Euler equations, with further development of the kinetics of the top
Derivation of the Euler equations	p. 138
Analytic treatment of the force-free motion of the top	p. 147
On the meaning of the Euler equations and their relation to the equations of Lagrange	p. 154
Guidance of the top on a prescribed path. D'Alembert's principle	p. 162
Special development for the spherical top. Decomposition of the total resistance into an acceleration resistance and a deviation resistance	p. 169
The deviation resistance for regular precession of the symmetric top	p. 174
A new derivation of the deviation resistance for regular precession of the symmetric top. The Coriolis force	p. 180
Experimental demonstration of the deviation resistance. The top with one and two degrees of freedom	p. 190
Addenda and Supplements	p. 197
Translators' Notes	p. 207
References	p. 263
Index	p. 275
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