Heidelberg 2007 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 3: Klassische Feldtheorie, Klassische Mechanik und Grundlagen der Quantentheorie
MP 3.2: Talk
Tuesday, March 6, 2007, 14:30–15:00, KIP SR 2.404
Evaluation of Abelian Integrals - Actions of the Kovalevskaya Top — •Dennis Lorek1,2 and Peter Richter2 — 1ZARM, Universität Bremen, Am Fallturm, 28359 Bremen — 2Institut für Theoretische Physik, Universität Bremen
The theory of Abelian integrals is one of the great achievements of the 19th century mathematics and has become a powerful tool in the physics of integrable systems. As an example, we discuss the Kovalevskaya case of rigid body dynamics which in its combination of mathematical beauty and physical complexity is perhaps the most fascinating integrable system of classical mechanics. An expression of its actions in terms of an Abelian integral was worked out previously, but their explicit computation and evaluation for an action representation of the energy surface has been lacking so far. This has now been achieved. We present the results which agree with the numerical work of Dullin and Wittek. This sort of representation is a highly convenient starting point for studies of stability against non-integrable perturbations, and for semi-classical quantization.