相关论文: An Analytical Solution of the Equations of a Rolli…

We present a systematic, analytical study of geometrically thin, optically thick accretion disc solutions for magnetized turbulent flows, with an alpha-like viscosity prescription. Under the only assumptions that (1) Magneto-Rotational…

A class of exact general relativistic rotating thick disks surrounded by rotating dust is constructed by applying the ``displace, cut, fill and reflect'' method on the van Stockum class of metrics. Two particular solutions are considered in…

The radial collapse of a homogeneous disk of collisionless particles can be solved analytically in Newtonian gravitation. To solve the problem in general relativity, however, requires the full machinery of numerical relativity. The collapse…

Axisymmetric accretion disks in vicinity of a central compact body are studied. For the simple models such as vertically isothermal disks as well as adiabatic ones the exact solutions to the steady-state MHD (magneto-hydrodynamic) system…

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these…

The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and…

The classical problem of steady rarefied gas flow past an infinitely thin circular disk is revisited, with particular emphasis on the gas behavior near the disk edge. The uniform flow is assumed to be perpendicular to the disk surface. An…

In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…

The one-dimensional, ordinary differential equation (ODE) by Hur\'e & Hersant (2007) that satisfies the midplane gravitational potential of truncated, flat power-law disks is extended to the whole physical space. It is shown that thickness…

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are…

We consider a class of fully self-gravitating accretion disks, for which efficient cooling mechanisms are assumed to maintain the disk close to the margin of Jeans instability. For such self-regulated disks the equations become very simple…

In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on…

We provide a description of a thin accretion disc for a static spherically symmetric black holes in $f(R)$ gravity. In this regard, we first study the horizons of black holes in $f(R)$ gravity. The equation of motion and effective potential…

We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…

Recent studies show interest in materials with asymmetric friction forces. We investigate terminal motion of a solid body with circular contact area. We assume that friction forces are asymmetric orthotropic. Two cases of pressure…

This paper proposes a Lagrangian approach to find the state equations of a disk rolling on a plane without friction. The approach takes advantage of a symbolic computation to simplify the reasoning.

We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local…

We study the ascending motion of a disk rolling on an incline when its center of mass lies outside the disk axis. The problem is suitable as laboratory project for a first course in mechanics at the undergraduate level and goes beyond…

In the present paper we study the geodesic motion of test particles and light rays in the spacetime of a static charged black hole in $f(R)$ gravity. The complete set of analytic solutions of the geodesic equations in the spacetime of this…