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在赤道同步卫星的运动中,轨道根数有着长周期的变化。本文利用广义相空间中的正则形式研究了24小时卫星运动的长周期特性,其中有:地球扁率、赤道椭率和日月摄动的影响。文中假定偏心率和倾角为小量(e<0.1,i<18°)。所有摄动公式是用一组非奇异的变量推导出来的,这纽变量类似于经典的庞加来变量。文章中引用的月球运动则是 Hill-Brown 月球运动理论。太阳的运动轨迹是围绕地球一月球质心的一个椭圆。本文在处理赤道椭率引起的谐振时,是把哈密顿函数对于参考半长轴进行 Bohlin 展开。
In the equatorial satellite movement, the number of orbits has a long period of change. In this paper, the long-period characteristics of 24-hour satellite motion are studied by the regular form in generalized phase space, including the flattening of the earth, the ellipticity of the equator and the influence of the sun and moon perturbations. It is assumed that eccentricity and dip are small (e <0.1, i <18 °). All perturbation formulas are derived from a set of non-singular variables that are similar to the classical Panga variable. The lunar movement quoted in the article is the theory of the Hill-Brown lunar movement. The sun’s trajectory is an ellipse around the lunar centroid of the Earth. In this paper, when dealing with the resonance induced by equatorial ellipticity, the Bohlin expansion of Hamiltonian to the reference semi-major axis is performed.