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     

Fundamentals of Celestial Mechanics

Book review

Fundamentals of Celestial MechanicsDanby, J. M. A.: 1988, Willmann-Bell, Inc., US $19.95 (softbound)     

天文动力学和天体力学

叙述了与Astrod工程有关的天体力学和天文动力学的基本结果和学科概况 ,内容包括二体问题、摄动理论、人造地球卫星运动、限制性三体问题等     

天体力学的几个热点问题

阐述当今天体力学前沿课题中的几个热点问题，近地小行星与地球的交会及其动力演化，航天器定轨新手段中的得一星跟踪自主定轨方法以及星际探测中的轨道力学问题。     

Celestial Mechanics and Dynamical Astronomy

Volume Contents

Celestial Mechanics and Dynamical Astronomy     

Momentum and Angular Momentum in the Expanding Universe

A new approach has been used to evaluate the momentum and angular momentum of the isotropic and homogeneous cosmological models. It is shown that the results obtained for momentum exactly coincide with those already available in the literature. However, the angular momentum expression coincides only for the closed Friedmann model.     

Celestial Mechanics and Dynamical Astronomy

Volume Contents

Celestial Mechanics and Dynamical Astronomy     

Spin Angular Momentum Imparted by Gravitational Waves

Following the demonstration that gravitational waves impart linear momentum, it is argued that if they are polarised they should impart angular momentum to appropriately placed ‘test rods’ in their path. A general formula for this angular momentum is obtained and used to provide expressions for the angular momentum imparted by plane and cylindrical gravitational waves. This revised version was published online in July 2006 with corrections to the Cover Date.     

Noncanonical Parametrization of Poisson Brackets in Celestial Mechanics

The formulas for the Poisson bracket of a perturbed two-body problem and a perturbed planetary problem are found in different systems of Keplerian elements. As with canonical parametrization, the Poisson bracket is equal to a linear combination of partial brackets, but it contains coefficients depending on semimajor axis, eccentricity, and inclination. A simple relation between the Poisson brackets and matrices of coefficients of Lagrange-type equations determining the variations of osculating elements is derived. The Poisson bracket of D'Alembertian functions is proved to be a D'Alembertian one by itself.     

盘状星系形成中的角动量问题

目前的星系形成理论认为，盘状星系由暗晕中的重子物质冷却并坍缩而成。在这一演化图像中，重子物质的角动量及其分布起着关键作用，它直接决定了盘状星系的结构。然而，在盘状星系形成和演化的各种解析、半解析模型及数值模拟中，出现了一系列与角动量有关的问题。其中包括角动量灾变(angular momentum catastrophe)及角动量分布不匹配(mismatch of angulamomentum profile)等。近年来，为解决此类问题，人们进行了大量的研究，引入并建立了各种机制和模型。详细表述了星系形成与演化中两类主要的角动量问题，并系统地综述了目前针对此类问题所提出的各种可能的解决方法和途径。     

Unsolved Problems of Celestial Mechanics — The Solar System

The Unsolved Problems of Celestial Mechanics for the Solar System are divided here into six distinct topics, (1) discrepancies between observations and ephemerides, (2) formation and stability of the solar system, (3) resonances, (4) theories, (5) reference systems, and (6) artificial satellites.This paper was presented as an invited paper at a session of Commission 7, Celestial Mechanics, at the IAU General Assembly in New Delhi, India, in November 1985.     

Viscoelastic tides: models for use in Celestial Mechanics

In this note, by using Smale’s \(\alpha \)-theorem on the convergence of Newton’s method, the \(\alpha \)-sets of convergence of some starters of solving the elliptic Kepler’s equation are derived. For each starter we compute the exact \(\alpha \)-set in the eccentricity-main anomaly \((e,M)\in [0,1)\times [0,\pi ]\), showing that these sets are larger than those derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014). Further, new convergence tests based on the Newton–Kantorowitch theorem are given comparing with the derived from Smale’s \(\alpha \)-test.