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 引用本文: 曹静, 袁建平, 罗建军. 陀螺进动与强迫进动轨道[J]. 力学学报, 2013, 45(3): 406-411.
Cao Jing, Yuan Jianping, Luo Jianjun. GYROSCOPIC PRECESSION AND FORCED PRECESSION ORBIT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 406-411.
 Citation: Cao Jing, Yuan Jianping, Luo Jianjun. GYROSCOPIC PRECESSION AND FORCED PRECESSION ORBIT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 406-411.

## GYROSCOPIC PRECESSION AND FORCED PRECESSION ORBIT

• 摘要: 陀螺进动与轨道进动现象的相似性归因于二者的动力学相似性. 通过类比二者的动力学模型,提出了一类强迫进动轨道. 若以圆轨道为初始轨道,通过施加常值法向力可以实现一种特殊的悬浮型强迫进动轨道. 采用四元数建模方法求解了这种强迫进动轨道的进动规律,给出了解析表达式,据此分析了这种轨道的性质. 分析结果表明这种强迫进动轨道与初始圆轨道在同一球面上,且与初始位置相切. 其角速度为进动角速度与初始轨道角速度的合成,是一种悬浮轨道,即属于非开普勒轨道. 悬浮轨道在地球观测、行星际科学、天文观测、无线电通讯以及地球工程等领域具有潜在应用前景. 从强迫进动的角度出发所作的分析为悬浮轨道的实现提供了一种新途径.

Abstract: The analogous precession phenomena of gyroscope and orbital plane are based on the dynamical similarity. In present paper a special kind of forced precession orbit is proposed through the comparison of dynamical models of gyroscope and orbital plane. When the initial orbit is a circular orbit, the forced precession orbit can be realized by the action of a constant normal control force. The characters of forced precession orbital motion are discussed using the mathematical model expressed by quaternion, and the analytical solutions are obtained. It is shown that the forced precession orbit and the initial orbit are laying on the same spherical surface, and they are tangent each other at the initial position. The angular velocity of the forced precession orbit is the summation of precession speed and the angular velocity of the initial orbit. The new orbit is a non-Keplerian displaced orbit, which has a potential perspective of applications in Earth observation, planetary science, observational astronomy, telecommunications and geo-engineering. The analysis from the view point of forced precession provides a new way to realize the displaced orbit.

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