Dynamics of Tethered Space Systems: 1st Edition (Paperback) book cover

Dynamics of Tethered Space Systems

1st Edition

By Hans Troger, A.P. Alpatov, V.V. Beletsky, V.I. Dranovskii, V.S. Khoroshilov, A.V. Pirozhenko, A.E. Zakrzhevskii

CRC Press

245 pages | 120 B/W Illus.

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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



About the Authors

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.

About the Series

Advances in Engineering Series

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