地磁场中刚体卫星的混沌运动

讨论了地球磁场中沿赤道平面圆轨道运行的非对称磁性刚体卫星的姿态运动．引入Ｄｅｐｒｉｔ变量建立系统的Ｈａｍｉｌｔｏｎ结构．利用Ｈｏｌｍｅｓ和Ｍａｒｓｄｅｎ发展了的Ｍｅｌｎｉｋｏｖ方法分析混沌存在的可能性，导出在一定的参数条件下刚体的运动为Ｓｍａｌｅ马蹄意义下混沌运动的结论．数值计算表明，混沌区域随着卫星磁矩的增加而扩大

Chaotic Motion of a Rigid-Body Satellite in the Magnetic Field of the Earth

The attitude motion of an asymmetric magnetric rigid body on a circular orbit in the equator plane subjected to the magnetic torque of the earth was investigated by using the version of Melnikov's method developed by Holmes and Marsden. For this purpose, Deprit's variables were introduced to establish the Hamiltonian structure for this problem. It is found that the motion is chaotic in the sense of Smale's horseshoe for certain parameter range. The numerical simulations show that, as the magnetism of the satellite increases, the chaotic area enlarges.