The Theory of the Top. Volume II Development of the Theory in the Ca
The Theory of the Top. Volume II. Development of the Theory in the Case of the Heavy Symmetric Top is the second in a series of four self-contained English translations of the classic and definitive treatment of rigid body motion. Key features: * Complete
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Felix Klein Arnold Sommerfeld
The Theory of the Top Volume II
Development of the Theory in the Case of the Heavy Symmetric Top
Translated by Raymond J. Nagem Guido Sandri
Felix Klein Arnold Sommerfeld
The Theory of the Top Volume II Development of the Theory in the Case of the Heavy Symmetric Top Raymond J. Nagem Guido Sandri Translators
Preface to Volume I by Michael Eckert
Birkh¨auser Boston • Basel • Berlin
Raymond J. Nagem Boston University Boston, MA 02215 USA [email protected]
Guido Sandri Boston University Boston, MA 02215 USA [email protected]
ISBN 978-0-8176-4824-4 e-ISBN 978-0-8176-4827-5 DOI 10.1007/978-0-8176-4827-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010928631 Mathematics Subject Classification (2010): 01A75, 33E05, 70E05, 70E15, 70E17, 70E18, 70E40, 70E45, 70E50
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Contents
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Volume II. Development of the Theory in the Case of the Heavy Symmetric Top.
Chapter IV. The general motion of the heavy symmetric top. Introduction to elliptic integrals. §1. Intuitive discussion of the expected forms of motion; preliminary agreements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 §2. Intuitive discussion of the expected forms of motion; continuation and conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 §3. Quantitative treatment of the general motion of the heavy symmetric top. Execution of the six required integrations. . . . 216 §4. General periodicity properties of the motion. Preliminaries on the behavior of the elliptic integrals for a circulation of the integration segment. Integral representation of α, β, γ, δ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 §5. On the relation between the motions of different tops that yield the same impulse curve, and on the motion of the spherical top. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 §6. 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. . .
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