# Analytical Solution of the Perturbed Oribt-Attitude Motion of a Charged Spacecraft in the Geomagnetic Field

• M. H
• K. M
• Owis A
• et al.
N/ACitations

#### Abstract

In this work we investigate the orbit-attitude perturbations<br />of a rigid spacecraft due to the effects of several forces<br />and torques. The spacecraft is assumed to be of a cylindrical<br />shape and equipped with a charged screen with charge density<br />s. Clearly the main force affecting the motion of the spacecraft<br />is the gravitational force of the Earth with uniform spherical<br />mass. The effect of oblate Earth up to J2 is considered as<br />perturbation on both the orbit and attitude of the spacecraft,<br />where the attitude of the spacecraft is acted upon by what is<br />called gravity gradient torque. Another source of perturbation<br />on the attitude of the spacecraft comes from the motion of<br />the charged spacecraft in the geomagnetic field. This motion<br />generates a force known as the Lorentz force which is the source<br />of the Lorentz force torque influencing the rotational motion of<br />the spacecraft. In this work we give an analytical treatment of<br />the orbital-rotational dynamics of the spacecraft. We first use<br />the definitions of Delaunay and Andoyer variables in order to<br />formulate the Hamiltonian of the orbit-attitude motion under the<br />effects of forces and torques of interest. Since the Lorentz force<br />is a non-conservative force, a potential like function is introduced<br />and added to the Hamiltonian. We solve the canonical equations<br />of the Hamiltonian system by successive transformations using a<br />technique proposed by Lie and modified by Deprit and Kamel<br />to solve the problem. In this technique we make two successive<br />transformations to eliminate the short and long periodic terms<br />from the Hamiltonian.

#### Cite

CITATION STYLE

APA

M., H., K., M., Owis, A., & Dwidar, H. (2013). Analytical Solution of the Perturbed Oribt-Attitude Motion of a Charged Spacecraft in the Geomagnetic Field. International Journal of Advanced Computer Science and Applications, 4(3). https://doi.org/10.14569/ijacsa.2013.040341

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