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 TETHERED SYSTEMS IN SPACE: A SHORT INTRODUCTION 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 EQUATIONS OF MOTION OF SPACE TETHER SYSTEMS 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 ANALYSIS OF THE MOTION OF TSS 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 USE OF RESONANCE FOR MOTION CONTROL Introductory remarks: Formulation of the problem Control of motion of the system around its mass centre Control of orbital motion DEPLOYMENT OF TETHERED SPACE SYSTEMS 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 Bibliography Index
Vienna University of Technology, Vienna, Austria Institute of Technical Mechanics NAS&NSA of Ukraine, Dnepropetrovsk, Ukraine Keldysh Institute of Applied Mathematics, RAN, Moscow, Russia NSA of Ukraine, Youzhnoye State Design Office The Yangel State Design Office Yuzhnoye , Dnepropetrovsk, Ukraine Institute of Technical Mechanics NAS&NSA of Ukraine, Dnepropetrovsk, Ukraine S. P. Timoshenko Institute of Mechanics NAS of Ukraine, Kiev, Ukraine