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ЖУРНАЛЫ // Theoretical and Applied Mechanics // Архив

Theor. Appl. Mech., 2017, том 44, выпуск 2, страницы 229–236 (Mi tam31)

Эта публикация цитируется в 3 статьях

Discriminantly separable polynomials and the generalized Kowalevski top

Vladimir Dragovichab, Katarina Kukićc

a The Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, USA
b Mathematical Institute SANU, Belgrade, Serbia
c Faculty for Traffic and Transport Engineering, University of Belgrade, Belgrade, Serbia

Аннотация: The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski's original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top — the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.

Ключевые слова: the generalized Kowalevski top, discriminantly separable polynomials, separation variables.

MSC: Primary 37J35, 37K60; Secondary 70E17, 70E40, 39A10

Поступила в редакцию: 26.09.2017
Исправленный вариант: 15.11.2017

Язык публикации: английский

DOI: 10.2298/TAM170926016D



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