245 Pages 120 B/W Illustrations
    by CRC Press

    246 Pages 120 B/W Illustrations
    by CRC Press

    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.

    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



    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.