The Theory of the Top

The Theory of the Top: Volume II. Development of a Theory of the Heavy Symmetric Top is the second installment of a series of four self-contained English translations of the classic and definitive treatment of rigid body motion.Key features:* Complete and unabridged presentation with recent advances and additional notes* Annotations by the translators provide insights into the nature of science and mathematics in the late 19th century* Each volume interweaves theory and applicationsThe Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this a thorough and insightful account. Other volumes in this series include Introduction to the Kinematics and Kinetics of the Top, Perturbations: Astronomical and Geophysical Applications, and Technical Applications of the Theory of the Top.

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Development of the Theory in the Case of the Heavy Symmetric Top.
The general motion of the heavy symmetric top. Introduction to elliptic integrals.
Intuitive discussion of the expected forms of motion; preliminary agreements	p. 197
Intuitive discussion of the expected forms of motion; continuation and conclusion	p. 204
Quantitative treatment of the general motion of the heavy symmetric top. Execution of the six required integrations	p. 216
General periodicity properties of the motion. Preliminaries on the behavior of the elliptic integrals for a circulation of the integration segment. Integral representation of ¿, ß, ¿, ¿	p. 224
On the relation between the motions of different tops that yield the same impulse curve, and on the motion of the spherical top.	p. 231
Confirmation of the forms of motion of the spherical top developed in the first sections; the characteristic curves of the third order in the case e = 0.	p. 239
The characteristic curves of the third order for arbitrary position of the initial circle e; distinction between strong and weak tops	p. 247
On the numerical calculation of the elliptic integrals for t and ¿	p. 259
On the approximate calculation of the top trajectories	p. 269
On special forms of motion of the heavy symmetric top, particularly pseudoregular precession, and on the stability of motion.
Regular precession and its neighboring forms of motion	p. 279
Pseudoregular precession; resolution of the paradoxes of the motion of the top	p. 291
Popular explanations of the phenomena of the top in the literature	p. 307
On the stability of the upright top. Geometric discussion	p. 316
Continuation. Analytic treatment of the motion of the upright top altered by an impact.-Formulas for pseudoregular precession with small precession circle	p. 326
Generalities on the stability and lability of motion	p. 342
Energy criteria for the stability of equilibrium and motion	p. 354
On the method of small oscillations	p. 364
On the motion of the heavy asymmetric top.	p. 374
Representation of the motion of the top by elliptic functions.
The Riemann surface (u, √U)	p. 392
Behavior of the elliptic integrals on the Riemann surface	p. 397
The image of the Riemann surface (u, √U) in the t-plane	p. 406
Representation of ¿, ß, ¿, ¿ by v-quotients	p. 417
The trajectory of the apex of the top, the polhode and herpolhode curves, etc., represented by v-quotients	p. 430
Numerical calculation of the motion by v-series	p. 440
Representation of the motion of the force-free top by elliptic functions	p. 454
Conjugate Poinsot motions. Jacobi's theorem on the relation between the motion of the force-free asymmetric top and the heavy spherical top	p. 476
The Lagrange equations for ¿, ß, ¿, ¿ of the heavy spherical top and their direct integration. Relation between the motion of the spherical top and a problem in particle mechanics	p. 491
Appendix to Chapter VI.
The top on the horizontal plane	p. 513
Addenda and Supplements	p. 533
Translators' Notes	p. 543
References	p. 593
Index	p. 603
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