Chandrasekhar's perturbation method-oriented theories up to third order for uniformly and differentially-rotating polytropic stars: Error-removing techniques

In this paper we analyse error-removing techniques used without sufficient theoretical support in a previous paper, where Chandrasekhar's higher-order perturbation theories were developed for either uniformly or differentially-rotating polytropic stars.     

Application of a global polytropic model to the Jupiter's system of satellites: a numerical treatment

We study the so-called inverse planetary problem (i.e., given the distances from the centre, masses, and radii of, say, three planets of a planetary system, find the optimum polytropic index, mass, and radius of their star, and also other quantities of interest, which depend either explicitly or implicitly on the foregoing ones, e.g., central and mean density, central and mean pressure, central and mean temperature, etc.) for the system of satellites of Jupiter. In particular, Jupiter is considered as star and its satellites as planets of a proper planetary system, which is then treated numerically on the basis of the so-called global polytropic model, developed recently by the first author.     

The inverse planetary problem: a numerical treatment

The so-called inverse planetary problem can be stated as follows: given the distances from the centre, masses, and radii of (say) three planets of a planetary system, find the optimum polytropic index, mass, and radius of their star, and also other quantities of interest, which depend either explicitly or implicitly on the foregoing ones (e.g., central and mean density, central and mean pressure, central and mean temperature, etc.). It is hereafter tacitly assumed that the system is opaque with respect to observations concerning periods of planetary otbits; hence, we cannot have any relevant estimates due to the well-known period laws. In the present paper, the inverse planetary problem is treated numerically on the basis of the so-called global polytropic model, developed recently by the first author.     

Models of white dwarfs distorted by magnetic field and differential rotation: Numerical approach

In this paper we construct a generalized classical model of a white dwarf distorted by magnetic field and differential rotation. The numerical method, to be presented, will be implemented in a subsequent quantitative treatment of the model.     

Differentially rotating gaseous polytropes: construction of a solar model with constant mass

Differentially rotating polytropic configurations are considered by assuming that their masses are constant. Structure parameters and related quantities of interest, characterizing a solar model and computed by purely numerical methods, are compared with their respective values obtained when the central densities of the configurations of the model are assumed equal.This research was supported by the Research Development Project of the University of Patras, Greece.     

Clarification on the law of angular momentum

In most courses on continuum mechanics the law of angular momentum is studied about a fixed point (usually about the origin of the frame). In this article we clarify this law about any point in three-dimensional Euclidean space and discuss the law, about any point, for an observer in a rotating frame.     

Zatrikean pre-geometry: number of alyssoids and the dilation factors

This paper is the continuation of a recent paper (written by the first author), in which an axiomatic zatrikean (i.e., chess-like) pre-geometry together with a rotationally induced zatrikean pre-geometry were developed. In the present paper, the number of alyssoids joining two geobits is determined for bothQ andR pre-metrics. Furthermore, the functional forms ofQ andR pre-geometric dilation factors are determined and calculated. It has been verified that these functions contain discontinuities and, therefore, a method for smoothing them out is proposed and applied.     

Rotational dynamics of a deformable medium

The aim of the present investigation has been to derive from the fundamental Cauchy's first law of continuum mechanics the explicit form of the Eulerian general equation which governs the three-axial generalized rotation about the centre of mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian) or not, consisting of compressible fluid of arbitrary viscosity, in an external field of force. The generalized rotation is a superposition of the so-called rigid-body (i.e., time dependent only) rotation of the continuum plus a nonrigidbody (i.e., position-time dependent) rotation of its configurations.In Section 2, which follows brief introductory remarks outlining the problem, we develop a mathematical theory which describes the whole phenomenon in terms of two rotation tensors corresponding, respectively, to the rigid-body and nonrigid-body rotation modes. In Section 3, we derive the differmation vectors of velocity and acceleration. The equations we have obtained are a very general version of Navier Stokes' equations, which were not given in previous investigations. In Section 4, we perform integration of the left-hand side of Cauchy's first law, cross-multiplied by the position vector, without any restriction. In Section 6, integration of the right-hand side of the same law, cross-multiplied by the position vector, is carried out, by taking account of actually simplifying assumptions stated in Section 5. All the integral terms occurring in both sides are expressed explicitly by quantities evaluated in terms of components of properly defined moments.Finally, in Section 7, the system of the general Eulerian equations is set up; and some easy modifications are given, which describe nicely physical models of special interest; while the concluding Section 8 contains a general discussion of the results.     

The Eulerian equations of differentially rotating gaseous polytropes

In this paper, we present in detail the whole process by which the Eulerian general equation is obtained, holding in case of a differentially rotating gaseous polytrope. The explicit form of this equation is derived on the basis of a model developed in a previous investigation.     

Models of white dwarfs under rapid uniform or differential rotation; numerical approach: The approximative phase

In this paper, we extend and generalize Chandrasekhar's perturbation method on rotating white dwarfs. In particular, we include terms up to third-order in the perturbation parameter, in order to study rapid and critical rotations. We also construct a generalized model of rotation which includes as subcases both uniform and differential rotations. The numerical method, described in the present paper, is required for a subsequent quantitative treatment of the particular problem.