Arnold Sommerfeld

The Theory of the Top. Volume IV. Technical Applications of the Theory of the Top is the fourth and final volume in a series of 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 applications. The 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 series of books a thorough and insightful account. Other volumes in the series include Introduction to the Kinematics and Kinetics of the Top, Development of the Theory in the Case of the Heavy Symmetric Top, and Perturbations. Astronomical and Geophysical Applications.

The Theory of the Top. Volume IV. Technical Applications of the Theory of the Top is the fourth and final volume in a series of 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 applications. The 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 series of books a thorough and insightful account. Other volumes in the series include Introduction to the Kinematics and Kinetics of the Top, Development of the Theory in the Case of the Heavy Symmetric Top, and Perturbations. Astronomical and Geophysical Applications.

Am 6. Dezember 1915 und am 8. Januar 1916 legte Arnold Sommerfeld der Bayerischen Akademie der Wissenschaften zwei Abhandlungen im Umfang von 75 Druckseiten vor, mit denen er das Bohrsche Atommodell aus dem Jahr 1913 zur Bohr-Sommerfeldschen Atomtheorie erweiterte. In Sommerfelds Gesammelten Schriften findet sich nur die im Juli 1916 von Sommerfeld in den Annalen der Physik eingereichte Publikation daru¨ber. "Meine Spektrallinien sind endlich in der Akademie in’s Unreine gedruckt. In den Annalen werden sie in geläuterter Form erscheinen", so hatte Sommerfeld am 10. Februar 1916 dem Herausgeber der Annalen der Physik diese Publikation angeku¨ndigt. Aus wissenschaftshistorischer Sicht sind fu¨r die Erweiterung der Bohrschen Atomtheorie jedoch gerade die vor dem Läuterungsprozess publizierten Akademieabhandlungen von besonderem Interesse. Der Reproduktion dieser Akademieabhandlungen wird ein ausfu¨hrlicher physikhistorischer Essay (ca. 100 Druckseiten) vorangestellt.

Arnold Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld's work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics.

The Theory of the Top: Volume III. Perturbations: Astronomical and Geophysical Applications is the third installment in 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 series of books a thorough and insightful account. Other volumes in the series include the Introduction to the Kinematics and Kinetics of the Top, Development of a Theory of the Heavy Symmetric Top, and Technical Applications of the Theory of the Top.

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 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 applications The first volume established the general kinematic and kinetic foundations of the theory. Volume II discusses the motion of the symmetric top with a fixed support point, under the influence of gravity, in all its details. The 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 works in this series include Volume I. Introduction to the Kinematics and Kinetics of the Top, Volume III. Perturbations. Astronomical and Geophysical Applications, and Volume IV. Technical Applications of the Theory of the Top.

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 “idiosyncratic disposition,” 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 “almost no use was made of the theoretical framework developed atthebeginning”[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.

Arnold Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld's work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics.