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 引用本文: 杨梦洁, 袁建平. 一种改进的轨道动力学模型[J]. 力学学报, 2015, 47(1): 154-162.
Yang Mengjie, Yuan Jianping. AN IMPROVED MODEL OF ORBITAL DYNAMICS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 154-162.
 Citation: Yang Mengjie, Yuan Jianping. AN IMPROVED MODEL OF ORBITAL DYNAMICS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 154-162.

## AN IMPROVED MODEL OF ORBITAL DYNAMICS

• 摘要: 航天器的矢径可以分解为矢径模和单位矢量的乘积,利用该性质将传统轨道动力学方程分解为矢径模和矢径方向的动力学方程组,实现了航天器位置信息的分离;针对两个方程分别采用常数变易法和四元数描述方法,将轨道动力学模型转化为线性无奇异的方程组,同时得到了7 个新轨道变量,且建立了新轨道变量与惯性系下航天器位置速度信息以及轨道六要素之间的相互转换关系. 该轨道模型适用于任意形式的推力和摄动,避免了奇异性,且在虚拟时间的意义下,航天器的旋转角速度只取决于法向力;在常值推力和变推力的情况下,对该模型进行了数值验证,验证了新模型的可适用性、数值稳定性以及计算精度高的优势.

Abstract: The radius vector of spacecraft can be decomposed into the product of the mold and the unit vector. Using this property, the traditional orbital dynamics equation can be transformed into two equations which describe the mold's and direction's motions separately. The mold's equation can be converted to a linear equation without singularity by introducing the inverse of the mold; and using the variation of constants method, the linear equation can be reduced to one-order. As for the direction's equation, the quaternion description is suitable. This equation can be completely solved. Through the above handling methods, we obtain a new orbital dynamic model which contains seven equations. In the sense of the virtual time, the angular velocity of the spacecraft depends only on the normal force. This new orbital model is applicable to any form of thrust or perturbation. At the same time, we get seven new stable variables which completely equivalent to the kepler elements. And the transforming relationship has been established. In the end of this article, we verify the accuracy and applicability of the new model in the cases of constant and variable thrusts.

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