Abstract
The stability of a rotating dust cylinder against perturbations located in the plane perpendicular to the axis of rotation is investigated. It is shown that a homogeneous rotating cylinder containing a weak inhomogeneity is stable against such perturbations. A weakly inhomogeneous cylinder with opposite streams of equal density is unstable for thel=2 mode in the case of a perturbation of the form∼ei(lϕ−ωt), when the density increases radially. The instability of a system consisting of a homogeneous rotating dust cylinder in a hot homogeneous medium is determined. It is shown that the maximum growth rate corresponds tol = 2 when the density of a cold cylinder is not negligible in comparison with the density of the medium. In the opposite case, the maximum growth rate shifts toward l=3. An attempt is made to associate the existence of the maximum growth rate for l=2 with the presence of two spiral arms in most galaxies. It is shown that, when the longitudinal temperature is high enough, a rotating cylinder which is bounded in the radial direction is stable against arbitrary perturbations.
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol.10, No. 3, pp. 3–11, May–June, 1969.
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Bisnovatyi-Kogan, G.S., Zel'dovich, Y.B., Sagdeev, R.Z. et al. Theory of gravitational stability of a rotating cylinder. J Appl Mech Tech Phys 10, 333–341 (1969). https://doi.org/10.1007/BF00916158
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DOI: https://doi.org/10.1007/BF00916158