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1.
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. 相似文献
2.
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. 相似文献
3.
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. 相似文献
4.
J. N. Tokis 《Astrophysics and Space Science》1975,35(1):L27-L32
We attempt to derive the conditions for which the motion of a system of two deformable (fluid or not) bodies can be reduced to the well-known two-body problem. The new condition is discussed for some pairs of such bodies existing in the natural world. 相似文献
5.
J. N. Tokis 《Astrophysics and Space Science》1988,144(1-2):291-301
An exact solution of the free-convection flow near an infinite vertical plate moving in a rotating medium in the presence of foreign mass and a transverse magnetic field is presented under a constant heating of the plate. It is apparent from this solution that the effects of the motion, the temperature, and the mass transfer are linear and, hence, can be studied independently. Three applications of physical interest are discussed. The non-magnetic case and non-rotating case are are also discussed.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, on 30 May 1988. 相似文献
6.
The unsteady free-convection flow of an electrically-conducting fluid near an oscillating vertical plate of infinite extent, is studied in the presence of a uniform transverse magnetic field. Exact solutions for velocity, temperature and skin friction are obtained with the aid of the Laplace transform method, when the plate is oscillating harmonically in its own plane. The influence of various parameters, entering into the problem, is discussed for the velocity field and skin-friction. 相似文献
7.
J. N. Tokis 《Astrophysics and Space Science》1974,31(2):349-362
The aim of the present paper will be to derive an equation of dissipation of energy for a rotating body of arbitrary viscosity distorted by tides, which arise from the gravitational field of its companion in a close pair of such bodies.By a transformation of the fundamental equation of energy dissipation in terms of velocity of tidal deformation (Section 2), the dissipation function is constructed for a tidally-distorted body (Section 3). From this equation, the rate of dissipation of tidal energy is formulated for a nearly-spherical rotating body distorted by second harmonic longitudinal tides (Section 4); the coefficients of viscosity (or the bulk modulus) are treated as arbitrary functions of spatial coordinates. Finally (Section 5), expressions for the total energy dissipation within the orbital cycle are given for axial rotation of the distorted body, provided its angular velocity is constant (for example, with the Keplerian angular velocity).Research financed in part by the Division of Scientific Research and Development of Ministry of Sciences and Culture of Greece. 相似文献
8.
J. N. Tokis 《Astrophysics and Space Science》1992,191(1):131-135
The aim of this paper is to discuss systematically two numerical methods that can play the significant role of numerical simulators of stability in the corresponding astrophysical problems to which they are applied. 相似文献
9.
J. N. Tokis 《Astrophysics and Space Science》1978,58(1):167-174
The unsteady flow near an infinite flat plate, which is oscillating harmonically in its own plane, is studied in the presence of a magnetic field subjected to suction or injection. The magnetic field is perpendicular to the plate and the flow of viscous incompressible and electrically conducting fluid is regarded as being initially at rest. Exact solutions for velocity and skin-friction are obtained for the magnetic field fixed to the fluid or to the plate. 相似文献
10.
J. N. Tokis 《Astrophysics and Space Science》1985,112(2):413-422
The unsteady free-convection flow of an electrically-conducting fluid near a moving vertical plate of infinite extent is investigated in the presence of uniform transverse magnetic field fixed to the fluid or to the plate. Exact solution of this problem is obtained with the aid of the Laplace transform technique, when the plate is moving with a velocity which is an arbitrary functiuon of time. The solution is exemplified for three particular cases of physical interest; the non-magnetic case is also discussed. 相似文献