Periodic solutions for rotational motion of an axially symmetric charged satellite

Abstract

The present paper is devoted to the investigation of sufficient conditions for the existence of periodic solutions in the vicinity of stationary motion of a charged satellite in elliptic orbit. Lorentz forces which result from the motion of a charged satellite relative to the magnetic field of the Earth are considered. An axial symmetry is assumed about the center of mass of the satellite. In addition to the Lorentz force the perturbation caused by gravitational and magnetic fields of the Earth are considered. The stationary solutions and periodic orbits close to them are obtained using the Lyapunov theorem of holomorphic integral. Numerical results are used to explain the periodic motion of a certain satellite. It is shown that the charge-to-mass ratio has a significant influence on the periodic motion of satellites.

Attitude dynamics and control of spacecraft using geomagnetic Lorentz force

“…The spacecraft orbits accelerated by the Lorentz force are termed Lorentz -augmented orbits, because Lorentz force cannot completely replace the traditional rocket propulsion. Many authors introduced Lorentz force as perturbations on the orbital motion and formation flying such as in Vokrouhlicky (1989), Abdel-Aziz (2007a), Streetman and Peck (2007), Hiroshima et al (2009) , Gangestad et al (2010), and Abdel-Aziz and Khalil (2014).…”

“…Orbits of a spacecraft accelerated by the Lorentz force are termed Lorentz-augmented orbits, because the Lorentz force cannot completely replace traditional rocket propulsion. Many authors introduced using the Lorentz force to generate perturbations on the orbital motion and formation flying such as in Vokrouhlicky (1989), Abdel-Aziz (2007a), Streetman & Peck (2007), Hiroshi et al (2009), Gangestad et al (2010) and Abdel-Aziz & Khalil (2014). Abdel-Aziz (2007b) studied the attitude stabilization of a rigid spacecraft moving in a circular orbit due to Lorentz torque in the case of a uniform magnetic field and a spacecraft having a cylindrical shape.…”