Search results for "classical mechanics"
showing 10 items of 1211 documents
Dynamics of thick discs around Schwarzschild-de Sitter black holes
2003
We consider the effects of a cosmological constant on the dynamics of constant angular momentum discs orbiting Schwarzschild-de Sitter black holes. The motivation behind this study is to investigate whether the presence of a radial force contrasting the black hole's gravitational attraction can influence the occurrence of the runaway instability, a robust feature of the dynamics of constant angular momentum tori in Schwarzschild and Kerr spacetimes. In addition to the inner cusp near the black hole horizon through which matter can accrete onto the black hole, in fact, a positive cosmological constant introduces also an outer cusp through which matter can leave the torus without accreting on…
Relativistic simulations of rotational core collapse : I. Methods, initial models, and code tests
2002
We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3+1 formalism and a conformally flat metric approximation of the Einstein equations. The relativistic hydrodynamics equations are formulated as a first-order flux-conservative hyperbolic system and are integrated using high-resolution shock-capturing schemes based on Riemann solvers. We assess the quality of the conformally flat metric approximation for relativistic core collapse and present a comprehensive set of tests which the code successfully passed. The tests include relativistic shock tubes, the preservation of the rotatio…
The planar two-body problem for spheroids and disks
2021
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral, and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not invol…
Thouless-Valatin Rotational Moment of Inertia from the Linear Response Theory
2017
Spontaneous breaking of continuous symmetries of a nuclear many-body system results in appearance of zero-energy restoration modes. Such modes introduce a non-physical contributions to the physical excitations called spurious Nambu-Goldstone modes. Since they represent a special case of collective motion, they are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total angular momentum operator. We examine the role and effects of the pairing correlations on the rotational cha…
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
2009
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…
A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior
2013
Abstract This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations …
A gradient elasticity theory for second-grade materials and higher order inertia
2012
Abstract Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the …
Ejection and collision orbits of the spatial restricted three-body problem
1985
We begin by describing the global flow of the spatial two body rotating problem, μ=0. The remainder of the work is devoted to study the ejection and collision orbits when μ>-0. We make use of the ‘blow up’ techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S2×R. Also we find some particular collision-ejection orbits.
A class of shear deformable isotropic elastic plates with parametrically variable warping shapes
2017
A homogeneous shear deformable isotropic elastic plate model is addressed in which the normal transverse fibers are allowed to rotate and to warp in a physically consistent manner specified by a fixed value of a real non-negative warping parameter ω. On letting ω vary continuously (at fixed load and boundary conditions), a continuous family of shear deformable plates Pω is generated, which spans from the Kirchhoff plate at the lower limit ω=0, to the Mindlin plate at the upper limit ω=∞; for ω=2, Pω identifies with the third-order Reddy plate. The boundary-value problem for the generic plate Pω is addressed in the case of quasi-static loads, for which a principle of minimum total potential …
Figures of equilibrium in close binary systems
1992
The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.