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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.
Using the Earth’s gravitational field model to calculate the disturbance gravitational force of the orbit of an aircraft, when the aircraft overflies the two poles and the vicinity thereof, the calculation of the disturbing gravitation will be infinite due to the first derivative of the Legendre function and the sine function of the residual latitude contained in the denominator. The formulas for calculating the first derivative of Legendre function and the singularity of spherical harmonic function mP nm (cos θ) / sin θ are deduced. The detailed calculation model for the non-singularity of the disturbance gravitational force of the orbit is established and the perturbation gravitation The trend of each component in the two polar regions, so as to completely solve the problem of the singularity when using the gravity model of the Earth to calculate the disturbing gravity of the orbit of a bipolar region.