弹道扰动引力无奇异性计算模型的建立

Construction of non-singular computational model of trajectory disturbing gravity

利用地球重力场模型来计算飞行器轨道扰动引力,当飞行器飞越两极及其附近地区时,由于Legendre函数的一阶导数以及分母上所含余纬的正弦函数,将导致扰动引力的计算出现无穷大.本文推导了Legendre函数一阶导数以及球谐函数mP nm(cosθ)/sinθ无奇异性的计算公式,建立了飞行器轨道扰动引力各分量无奇异性的详细计算模型,并通过数值试验分析了扰动引力各分量在两极地区的变化趋势,从而彻底解决了利用地球重力场模型计算两极地区飞行器轨道扰动引力时存在的奇异性问题.

If the trajectory disturbing gravity is computed by earth gravity field model, due to the first-order derivatives of the Legendre functions of the eolatitude and the sine function of colatitude in the denominator, the calcultated disturbing gravity values tend to be infinity when the missiles are flying around the poles. Therefore, the non-singular computational formulae of the first-order derivatives of the Legendre functions of the colatitude and the m P~ （cos0）/sin0 are deduced here. The non-singular particular computational models of each component of the trajectory disturbing gravity are constructed. Then, the changing trends of each component of trajectory disturbing gravity in polar regions are analyzed by numerical experiments, which show that the singular problem in the computation of trajectory disturbing gravity in polar regions by earth gravity field model is completely solved