Chaotic motion of an asymmetric gyrostat in the magnetic field of the earth

Abstract

Summary.The attitude motion of an asymmetric magnetic gyrostat satellite in a circular orbit subjected to both gravitational and magnetic forces of the earth is investigated by using the version of Melnikov's method developed for a two-degree of freedom Hamiltonian system with S 1 symmetry. For this purpose Deptrit's canonical variables are introduced to establish the Hamiltonian structure for this problem. It is found that the motion is chaotic in the sense of Smale's horseshoe under certain conditions. The effects of the magnetic moment of the gyrostat and the speed of the rotor in the gyrostat on the global motion are also studied by numerical computation. It is shown that as the magnetic moment of the gyrostat increases, the chaotic area in the Poincar~ map will enlarge; as the rotor speed increases, a chaotic motion will turn into a regular motion.

Chaotic attitude motion and its control of spacecraft in elliptic orbit and geomagnetic field

“…Beletsky et al [9,10] discussed the chaotic motion of a magnetic spacecraft in circular polar orbit without damping and gravitational torque numerically. Cheng, Chen and Liu [11][12][13] studied the chaotic motion of a magnetic spacecraft in a circular orbit by using the Melnikov method and found that the onset of chaos is characterized by the intermittence as the increase of the magnetic torque. In present paper, the planar libration of a spacecraft in an arbitrary elliptic orbit under the action of gravitational and magnetic torque of the earth is treated.…”