• Journal of Astronomy and Space Sciences
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• v.24 no.4
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• pp.315-326
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• 2007

Recently introduced, several explicit solutions of relative motion between neighboring elliptic satellite orbits are reviewed. The performance of these solutions is compared with an analytic solution of the general linearized equation of motion. The inversion solution by the Hill-Clohessy-Wiltshire equations is used to produce the initial condition of numerical results. Despite the difference of the reference orbit, the relative motion with the relatively small eccentricity shows the similar results on elliptic case and circular case. In case of the 'chief' satellite with the relatively large eccentricity, HCW equation with the circular reference orbit has relatively larger error than other elliptic equation of motion does.

• Journal of Astronomy and Space Sciences
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• v.25 no.3
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.1
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• pp.82-90
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• 2014

In this paper, the effect of Lorentz force on the stability of attitude orientation of a charged spacecraft moving in an elliptic orbit in the geomagnetic field is considered. Euler equations are used to derive the equations of attitude motion of a charged spacecraft. The equilibrium positions and its stability are investigated separately in the pitch, roll and yaw directions. In each direction, we use the Lorentz force to identify an attitude stabilization parameter. The analytical methods confirm that we can use the Lorentz force as a stabilization method. The charge-to-mass ratio is the main key of control, in addition to the components of the radius vector of the charged center of the spacecraft, relative to the center of mass of the spacecraft. The numerical results determine stable and unstable equilibrium positions. Therefore, in order to generate optimum charge, which may stabilize the attitude motion of a spacecraft, the amount of charge on the surface of spacecraft will need to be monitored for passive control.