Article,
Analytical Solution of the Perturbed Oribt-Attitude Motion of a Charged Spacecraft in the Geomagnetic Field
International Journal of Advanced Computer Science and Applications(IJACSA), (2013)
Abstract
In this work we investigate the orbit-attitude perturbations
of a rigid spacecraft due to the effects of several forces
and torques. The spacecraft is assumed to be of a cylindrical
shape and equipped with a charged screen with charge density
s. Clearly the main force affecting the motion of the spacecraft
is the gravitational force of the Earth with uniform spherical
mass. The effect of oblate Earth up to J2 is considered as
perturbation on both the orbit and attitude of the spacecraft,
where the attitude of the spacecraft is acted upon by what is
called gravity gradient torque. Another source of perturbation
on the attitude of the spacecraft comes from the motion of
the charged spacecraft in the geomagnetic field. This motion
generates a force known as the Lorentz force which is the source
of the Lorentz force torque influencing the rotational motion of
the spacecraft. In this work we give an analytical treatment of
the orbital-rotational dynamics of the spacecraft. We first use
the definitions of Delaunay and Andoyer variables in order to
formulate the Hamiltonian of the orbit-attitude motion under the
effects of forces and torques of interest. Since the Lorentz force
is a non-conservative force, a potential like function is introduced
and added to the Hamiltonian. We solve the canonical equations
of the Hamiltonian system by successive transformations using a
technique proposed by Lie and modified by Deprit and Kamel
to solve the problem. In this technique we make two successive
transformations to eliminate the short and long periodic terms
from the Hamiltonian.
