Dynamics of Tethered Space Systems  book cover
1st Edition

Dynamics of Tethered Space Systems

ISBN 9781138117938
Published June 14, 2017 by CRC Press
245 Pages 120 B/W Illustrations

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Book Description

During many of the earliest American and Russian space missions, experiments were performed using cables to connect people and objects to spacecraft in orbit. These attempts generated considerable information about the formation of tethered systems and basic problems with tether orientation and gravity-gradient stabilization. During the 1970s, interest in tethered space systems (TSS) came to the forefront with an international project that involved the hanging of a probe from a low-orbit satellite to collect data on the Earth and its atmosphere. Since that time, TSS has grown to become its own area of research.

Dynamics of Tethered Space Systems brings together the work of seven leading researchers working at the forefront of TSS. Together, they provide a brief yet thorough introduction to TSS. Then, combining theory with experimental approaches important to industry, they cover the dynamics of the mechanical, physical, and mathematical modeling approaches involved in tethered satellite deployment. They present several models from the literature, focusing on the simplest but most important system: two satellites in orbit around the Earth. Discussion then expands to cover more complex examples.

Along the way, the authors consider a number of important topics, such as energy production resulting from interaction between the system and Earth’s magnetic field and momentum transfer in relation to satellites, microgravity laboratories, and futuristic applications such as the space elevator. They also look at a number of challenges, including those with deployment and energy dissipation.

Providing approaches to theoretical models and experimental methods, the text includes a wealth of essential equations and detailed analyses of forces acting on tethered objects in motion. It provides both a starting point for further research and the tools needed to apply that research to the applications of tomorrow.

Table of Contents

Symbol Description
List of Figures
List of Tables

Basic features and areas of applications
Physical models of TSS in literature
Comparison of the influence of various physical effects
Gravitational perturbations
Bending and friction forces in the cable
Electromagnetic forces
Aerodynamic drag, solar radiation and impacts of micrometeorites
Methods of mathematical modelling
Basic model: Point masses connected by a massless string
Model of TSS with massive string: Tether equations; Satellite equations
Known results and some problems

Some remarks concerning the motion of TSS
Two point masses connected by a massless elastic string
Unperturbed motion
Equations of perturbed motion
System with an elastically attached mass
Motion of a mass point in the central force field
Relative motion of a tethered system
Motion about the orbit of the mass centre
Motion of the mass centre
On the derivation of new forms of equations of perturbed Keplerian motion

Regular attitude motions of TSS
On application of the averaging method
Influence of gravitational oscillations
Motion due to longitudinal oscillations of small amplitude
Motion with longitudinal oscillations of large amplitude 
Slow rotation of the system
Energy dissipation due to the tether material
Essentially non-linear longitudinal oscillations
Linear tether stretching
Averaging with respect to the phases of oscillations of the unperturbed motion
Phase of slow evolution:1st approximation longitudinal oscillations; Laws of motion
Influence of aerodynamic forces
Equations of first approximation
Influence of dissipative aerodynamic forces
Basic laws of evolution of motion
Influence of other perturbing factors
Interaction of translational and rotational motions
Equations of motion
First integrals
Basic laws of evolution of the system
Dissipation of energy due to the visco-elastic tether material
Regular and chaotic motions of TSS with inextensible tether
Chaotic motion of TSS with extensible tether
Statement of the problem
Qualitative analysis of attitude motion of an orbital pendulum w/ oscillating length
Analysis of a specific trajectory: Estimation of the variation of energy for pendulousmotions; Analysis of the character of the trajectory
Analysis of sets of trajectories
Non-linear resonances
Image of chaotic motions
Effect of energy dissipation
 Results of numerical calculations
Analysis of chaotic motions and their images

Introductory remarks: Formulation of the problem
Control of motion of the system around its mass centre
Control of orbital motion

Deployment with prescribed final motion
Prescribed constraints on phase variables
Prescribed trajectory
Monotonous tether feed out
Deployment of a rotating TSS 
Deployment due to gravitational and inertial forces
Deployment along an inclined direction to the local vertical
Deployment with changing of velocity of bodies after separation
Deployment of three elastically tethered bodies in the centrifugal force field 
Physical model
Mechanical model
Mathematical model
Numerical modelling of deployment
Experiment of unreeling the cable
Description of the experiment
Moment of inertia of a fly-wheel
Moment of friction forces in the bearings
Resistance force against unreeling of cable


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A.P. Alpatov is with the NAS and NSA of Ukraine. V.V. Beletsky is with Moscow State University, Russia. V.I. Dranovsky is with the NSA of Ukraine and the Youzhnoye State Design Office.