{"product_id":"polytropes-applications-in-astrophysics-and-related-fields-von-georg-p-horedt-1","title":"Polytropes","description":"\u003cp\u003eWhile it seems possible to present a fairly complete uni?ed theory of undistorted polytropes, as attempted in the previous chapter, the theory of distorted polytropes is much more extended and - phisticated, so that I present merely a brief overview of the theories that seem to me most interesting and important. Basically, the methods proposed to study the hydrostatic equilibrium of a distorted self-gravitating mass can be divided into two major groups (Blinnikov 1975): (i) Analytic or semia- lytic methods using a small parameter connected with the distortion of the polytrope. (ii) More or less accurate numerical methods. Lyapunov and later Carleman (see Jardetzky 1958, p. 13) have demonstrated that a sphere is a unique solution to the problem of hydrostatic equilibrium for a ?uid mass at rest in tridimensional space. The problem complicates enormously if the sphere is rotating rigidly or di?erentially in space round an axis, and\/or if it is distorted magnetically or tidally. Even for the simplest case of a uniformly rotating ?uid body with constant density not all possible solutions have been found (Zharkov and Trubitsyn 1978, p. 222). The sphere becomes an oblate ?gure, and we have no a priori knowledge of its strati?cation, boundary shape, planes of symmetry, transfer of angular momentum in di?erentially rotating bodies, etc.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048166459\"\u003e\u003ch3\u003eApplications in Astrophysics and Related Fields\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9789048166459","offer_id":39416480694365,"sku":"9789048166459","price":320.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/482bd142-124d-4966-8fac-8cb8e7aa66a3.jpg?v=1776233961","url":"https:\/\/shop.autorenwelt.de\/products\/polytropes-applications-in-astrophysics-and-related-fields-von-georg-p-horedt-1","provider":"Autorenwelt Shop","version":"1.0","type":"link"}