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The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The…
The sedimentation of a rigid particle near a wall in a viscous fluid has been studied numerically by many authors, but analytical solutions have been derived only for special cases such as the motion of spherical particles. In this paper…
Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…
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…
Determining the velocity field of structures such as galaxies, stars, and fluid planets is a relevant topic in astrophysics and astronomy. Depending on the shape of the astrophysical object, the internal velocity field may be obtained by…
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric stars under the additional assumption that it is composed of incompressible stratified fluid. The original system of…
Rigidity conditions for a body considered as a discrete system of relativistic particles are proposed. They by themselves do not yet determine an evolution of the system, and some second-order equations must be added to them.…
We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations…
The problem of a general, symmetric contact, between elastically similar bodies, and capable of idealisation using half-plane theory, is studied in the presence of interfacial friction. It is subject to a constant set of loads - normal…
We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable…
We present a formalism to obtain equilibrium configurations of uniformly rotating fluid in the second post-Newtonian approximation of general relativity. In our formalism, we need to solve 29 Poisson equations, but their source terms…
This work investigates different models of rotational dynamics of two rigid bodies with the shape of an ellipsoid, moving under their gravitational influence. The focus of this study is on their behavior, their linear stability, and…
This work aims at presenting the first two-dimensional models of an isolated rapidly rotating star that include the derivation of the differential rotation and meridional circulation in a self-consistent way.We use spectral methods in…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
Asteroid body-fixed hovering problem using nonideal solar sail models in a compact form with controllable sail area is investigated in this paper. The nonlinear dynamic equations for the hovering problem are constructed for a spherically…
The solution space of differentially rotating polytropes with n=1 has been studied numerically. The existence of three different types of configurations: from spheroids to thick tori, hockey puck-like bodies and spheroids surrounded by a…
We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. Firstly, we consider the relaxation…
We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field.…
Two dimensional realizations of self-consistent models for the ``perfect elliptic disks'' were tested for global stability by gravitational N-body integration. The family of perfect elliptic disk potentials have two isolating integrals;…