Abstract
In this paper, we provide an analytical study regarding the dynamics of a tethered satellite system, when the central gravitational field is generated by a variable mass object. We show that, in general, the equations of motion for the tethered satellite in the general case as well as in satellite approximation become different from the classical ones, provided that variable mass is considered. We also prove that these expressions could be reduced to the classical ones under the first Meshcherskii's law for variable mass. Moreover, we show that Meshcherskii's transformation is not valid for the dynamics of a dumbbell satellite system.
Highlights
At the end of nineteenth century, the concept of a Tethered Satellite Systems (TSS) was first established by Tsiolkovsky in 1895
We present an analytical study about the dynamics of the tethered satellite system when the central gravitational field is generated by an object whose variable mass
We prove that the tethered satellite equations of motion in general case and satellite approximation are different from the classical one when the variable mass is considered
Summary
At the end of nineteenth century, the concept of a Tethered Satellite Systems (TSS) was first established by Tsiolkovsky in 1895. Wong and Misra (2008) examined the planar dynamics of a wheel-and-spoke configured multi-spacecraft system, connected together by variable length tethers, near the second Sun–Earth Lagrangian point. Celletti and Sidorenko (2008) investigated the dumbbell satellite’s attitude dynamics, when the center of mass moves on a Keplerian trajectory They found a stable relative equilibrium position in case of circular orbits which disappears as far as elliptic trajectories are considered. There are several aspects of the dynamics of the tethered or dumbbell satellites systems are studied by many authors in the framework of both of them moves in a central gravity field generated by an object whose a constant mass. We will present analytical study about the tethered and dumbbell satellites systems dynamics when the central gravity field is created by a body whose variable mass. While the vector i denotes the position vector of mi with respect to the center of mass for the dumbbell satellite
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