UNIFORM ROTATIONS OF A TWO-BODY TETHERED SYSTEM IN AN ELLIPTIC ORBIT

Paper number

IAC-13,C1,1,6,x19742

Author

Prof. Anna Guerman, Centre for Mechanical and Aerospace Science and Technologies (C-MAST), Portugal

Coauthor

Dr. Alexander Burov, Dorodnitsyn Computing Center, Russian Academy of Sciences, Russian Federation

Coauthor

Prof. Ivan Kosenko, Dorodnitsyn Computing Center, Russian Academy of Sciences, Russian Federation

Year

2013

Abstract

Attitude control of spacecraft by changing its inertia parameters has been studied since 1960th [1]. Recently several efforts have been made to use this control for space system stabilization in elliptic orbits [2, 3].

Here we consider the motion of a dumbbell in a central gravitational field. The dumbbell consists of two material points connected by a massless rigid rod; the length of the rod can be changed according to a given law and is considered as a control function. The attraction center {\it N} is fixed; the motion occurs in a given plane that passes through {\it N}. If the dumbbell length is much less than the distance between its center of mass {\it C} and the attraction center {\it N}, the equations of motion for the center of mass separate from the equation of dumbbell attitude motion. Assuming that {\it C} moves along a Keplerian elliptic orbit and using true anomaly $\nu$ as an independent variable, one can write down the equations of the dumbbell’s attitude motion; these equations depend on the dumbbell length {\it L} and its derivative.

To obtain the control {\it L($\nu$)} that implements a given motion of the dumbbell, one should substitute the corresponding particular solution into the above equations and solve the resulting differential equation for {\it L($\nu$)}.

Here we are looking for a control law that results in a uniform, in terms of the true anomaly, in-plane rotation of the dumbbell. For some rotation frequencies (e.g., $\omega$ $=$ 0, +-1, +-2, … or $\omega$ $=$ 1/2, 3/2, …) such solutions can be found in closed form.

Analysis of stability for such rotations resulted in identification of intervals of stability both for direct ($\omega$$>$0) and inverse ($\omega$ $<$0) rotations; some of these intervals correspond to highly eccentric orbits.

References

[1] W. Schiehlen. Uber die Lagestabilisirung kunstlicher Satelliten auf elliptischen Bahnen. Diss. Dokt.-Ing. technische Hochschule Stuttgart. 1966.

[2] A. Burov, I. Kosenko, On planar oscillations of a body with a variable mass distribution in an elliptic orbit. J. Mech. Eng. Sci., 2011, vol. 225, no. 10, pp. 2288-2295.

[3] A. A. Burov, I.I. Kosenko, A.D. Guerman, Dynamics of a Moon-anchored tether with variable length, Advances in the Astronautical Sciences, 2012, Vol.142, pp. 3495-3507.

Abstract document

IAC-13,C1,1,6,x19742.brief.pdf

Manuscript document

IAC-13,C1,1,6,x19742.pdf (🔒 authorized access only).

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