Abstract
The problem of the equilibrium shape of a steady rotating rectilinear infinite cord of ideal self-gravitating homogeneous fluid is considered. The question whether, apart from the obvious solution, namely, an infinite circular cylinder, noncylindrical equilibrium figures can exist is investigated. A search is carried out among axisymmetric figures with periodic surface structure (“wavy” cylinders). The period of the wave structure and, in the first approximation, the shape of the surface are found as functions of the angular velocity of rotation.
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References
P. Appell,Figures of Equilibrium of a Rotating Homogeneous Fluid [Russian translation], ONTI, Moscow, Leningrad’ (1936).
S. Chandrasekhar,Ellipsoidal Figures of Equilibrium, New Haven University Press, London (1969).
A. Liapounoff,Sur les figures d’équilibre peu différentes des ellipsoides d’une masse liquide homogène douée d’un mouvement de rotation. Pt. 1. Étude Génerale du Problème, Acad. Impériale des Sci., St-Petersbourg (1906).
L. Likhtenshtein,Figures of Equilibrium of a Rotating Fluid [in Russian], Nauka, Moscow (1965).
L. N. Sretenskii, “Theory of figures of equilibrium of a rotating liquid mass,”Usp. Mat. Nauk, No. 5, 187 (1938).
Additional information
Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–30, May–June, 2000.
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Kuzin, A.K. Quasi-cylindrical figures of equilibrium of a rotating fluid. Fluid Dyn 35, 331–338 (2000). https://doi.org/10.1007/BF02697745
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DOI: https://doi.org/10.1007/BF02697745