磁性刚体航天器的混沌姿态运动

基金项目: 国家自然科学基金(10082003)

Chaotic Attitude Motion of a Magnetic Rigid Spacecraft

1.
Department of Mechanics, Shanghai University, Shanghai 200436, P. R. China;
2.
Shanghai Institute of Applied. Mathematics and Mechanics, Shanghai 200072, P. R. China;

摘要: 研究在地球万有引力场和磁场中的磁性刚体航天器在圆轨道上的混沌姿态运动。利用动量矩原理建立了系统的动力学模型。应用Melnikov方法证明了存在复杂非游荡Cantor集。分别采用时间历程、功率谱、Poincaré映射和Liapunov指数对系统动力学行为进行了数值研究。数值仿真表明,随着磁场力矩的增强,系统准周期环面破裂而出现混沌。
- 航天器姿态动力学 /
- 混沌 /
- Melnikov方法 /
- 数值仿真
Abstract: Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit of the earth is treated.The dynamical model of the problem was derived from the law of moment of momentum.The Melnikov analysis was carried out to prove the e}dstence of a complicated nonwandering Cantor set.The dynamical behaviors were numerically investigated by means of time history, Poincare map, power spectrum and Liapunov exponents.Numerical simulations indicate that the onset of chaos is characterized by break of torus as the increase of the tongue of the magnetic forces.
- charms /
- Melnikob’s method /
- numerical simulation /
- spacecraft attitude dynamics

[1]	Rimrott F J P.Introductory Attitude Dynamics[M].Berlin:Springer,1989,1-310.
[2]	刘延柱.航天器姿态动力学[M].北京:国防工业出版社,1995,1-347.
[3]	LIU Yan-zhu,CHEN Li-qun.Nonliear problems in spacecraft attitude dynamics[A].In: CHIEN Wei-zang Ed.Proc 3rd Int Conf Nonlinear Mech[C].Shanghai Univ Press,1998,80-86.
[4]	刘延柱,陈立群,成功,等.航天器姿态动力学中的稳定性、分岔和混沌[J].力学进展,2000,30(3):351-357.
[5]	Beletsky V V.Regular und Chaotisch Bewegung Sturrer Korper[M].Stuttgart:Teubner-Verlag,1995,31-65.
[6]	Beletsky V V,Pivoarov M L,Starostin E L.Regular and chaotic motions in applied dynamics of a rigid body[J].Chaos,1996,6(2):155-166.
[7]	CHEN Li-qun, LIU Yan-zhu, CHENG Gong.Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit near the equatorial plane[J].Journal of the Franklin Institute:Engineering and Applied Mathematics,2002,339(1):121-128.
[8]	CHEN Li-qun, LIU Yan-zhu.Chaotic attitude motion of a magnetic rigid spacecraft and its control[J].International Journal of Non-Linear Mechanics,2002,37(3):493-504.
[9]	刘延柱,陈立群.非线性动力学[M].上海:上海交通大学出版社,2002,217-225.
[10]	Wolf A,Swift J B,Swinney H L,et al.Determining Liapunov exponents from a time series[J].Physica D,1985,16(3):285-317.