相对论天体力学和后牛顿运动方程

叙述了与Astrod工程有关的相对论天体力学基础内容。包括相对论天体力学、广义相对论基本原理、PPN方法体系、PPN多体问题、PPN二体问题。高阶PN二体问题等     

On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target

2D numerical modelling of impact cratering has been utilized to quantify an important depth-diameter relationship for different crater morphologies, simple and complex. It is generally accepted that the final crater shape is the result of a gravity-driven collapse of the transient crater, which is formed immediately after the impact. Numerical models allow a quantification of the formation of simple craters, which are bowl-shaped depressions with a lens of rock debris inside, and complex craters, which are characterized by a structural uplift. The computation of the cratering process starts with the first contact of the impactor and the planetary surface and ends with the morphology of the final crater. Using different rheological models for the sub-crater rocks, we quantify the influence on crater mechanics. To explain the formation of complex craters in accordance to the threshold diameter between simple and complex craters, we utilize the Acoustic Fluidization model. We carried out a series of simulations over a broad parameter range with the goal to fit the observed depth/diameter relationships as well as the observed threshold diameters on the Moon, Earth and Venus.     

Short-lived asteroids in the 7/3 Kirkwood gap and their relationship to the Koronis and Eos families

A population of 23 asteroids is currently observed in a very unstable region of the main belt, the 7/3 Kirkwood gap. The small size of these bodies—with the notable exception of (677) Aaltje (∼30 km)—as well as the computation of their dynamical lifetimes (3<T_D<172 Myr) shows that they cannot be on their primordial orbits, but were recently injected in the resonance. The distribution of inclinations appears to be bimodal, the two peaks being close to 2° and 10°. We argue that the resonant population is constantly being replenished by the slow leakage of asteroids from both the Koronis (I∼2°) and Eos (I∼10°) families, due to the drift of their semi-major axes, caused by the Yarkovsky effect. Assuming previously reported values for the Yarkovsky mean drift rate, we calculate the flux of family members needed to sustain the currently observed population in steady state. The number densities with respect to semi-major axis of the observed members of both families are in very good agreement with our calculations. The fact that (677) Aaltje is currently observed in the resonance is most likely an exceptional event. This asteroid should not be genetically related to any of the above families. Its size and the eccentricity of its orbit suggest that the Yarkovsky effect should have been less efficient in transporting this body to the resonance than close encounters with Ceres.     

Validation of a finite difference method for the simulation of vortex-induced vibrations on a circular cylinder

The Karman Vortex Street generated by a circular cylinder is investigated by the numerical solution of the compressible Navier–Stokes equations in the incompressible Mach number range (Mach<0.3) using the Beam and Warming implicit scheme. The agreement with the fully incompressible projection method (Chorin, 1968) is fairly good while convergence time is very much better. The investigation suggests that the compressible Navier–Stokes equations may be used as an efficient alternative to study incompressible flows as well. Mach numbers just below 0.3 are enough to simulate incompressible flow behavior and at the same time do not cause numerical ill-conditioning in the solution. In addition, some relevant features of the vortices generated and carried by the wake of the cylinder could be fairly well captured.