相关论文: Celestial mechanics of elastic bodies II

In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory…

In this paper the effects of vibrations at high frequencies onto a freely falling two-body system in Schwarzschild spacetime are investigated. As reference motion of the same system without vibrations a circular orbit around the central…

There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value…

The influence of an arbitrary spin orientation on the quadrupolar structure of an extended body moving in a Schwarzschild spacetime is investigated. The body dynamics is described by the Mathisson-Papapetrou-Dixon model, without any…

The motion of an extended body up to the quadrupolar structure is studied in the Schwarzschild background following Dixon's model and within certain restrictions (constant frame components for the spin and the quadrupole tensor, center of…

This paper concerns the motion of relativistic strings in the Schwarzschild space-time. As a general framework, we first analyze the basic equations for the motion of a p-dimensional extended object in a general enveloping space-time (N;…

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…

A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…

We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…

Here we construct new solution for the Einstein equations -- some analog of the Schwarzschild metric in anti--de Sitter--Beltrami space in the $c\to \infty$ limit ($R$-space). In this case we derive an adiabatic invariant for finite…

We consider the problem of constructing static, elastic, many-body systems in Einstein gravity. The solutions constructed are deformations of static many-body configurations in Newtonian gravity. No symmetry assumptions are made.

Based on the covariant hamiltonian formalism, we study the dynamics of spinning test bodies in the Kerr and Schwarzschild spacetimes. For the first time, we derive the exact solution of circular orbits in the Kerr plane without truncating…

The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6]…

We investigate the physical properties of equilibrium sequences of non-self-gravitating surfaces that characterize thick disks around a rotating deformed compact object described by a stationary generalization of the static q-metric. The…

Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are…

We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit…

We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…

We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…

We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…