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The authors consider the problem of deployment in orbit of a small tether that can serve as a standard of length fiw calibration of both onboard and ground optical and radar tracking systems, as an integrated sensor of the force fields of planets, etc. A tether for two bodies is examined. Possible methods for compact placement of a tether in orbit in operating condition are discussed. The main method is that of use of the centrifugal fi~rces resulting from imparting to the tether an initial angular velocity in its deployment from the spacecraft. Various methods for creating moments of friction forces in hinges are considered. Numerical modeling of the dynamic processes is carried out within the framework of the theory of systems of bodies. Problems associated with determination of the required initial angular velocity and of the "cone of departure" of the tether from the spacecraft are examined. The use in space systems of bodies connected by long flexible tethers was suggested long ago by K. !~. Tsiolkovskii. Since then. a number of new possibilities have been proposed lbr the effective use of such systems to solve various scientific problems. This has made the development of tethers a promising field of modern space technology [ 1 ]. Although tethers with "'astronomical" dimensions have already been examined in theoretical studies, the principal attention of researchers is devoted to small tethers for systems that extend from a few meters to several kilometers with masses of from units to hundreds of kilograms [2, 4]. Such systems are of practical interest, since they are suitable for the solution of independent scientific problems as well as for full-scale working out and testing of hypotheses concerning the dynamics of tether deployment and the regimes of stationary tether motion. For example, a small rotary tether can serve as a standard of length tbr calibration of onboard and ground optical and radar measuring systems, integrated sensors of the force fields of planets, etc. One possible implementation of a small (on the order of several meters) tether between two bodies is a chain or a system of several bodies connected by cylindrical hinges. The end links of such a system contain elements whose masses determine the total mass of the system (Fig. 1) The problem of deployment of such a system to the maximum distance between the centers of mass of the end bodies can be solved in a number of ways. For example, actuators (energy source, final control elements, program or interactive control system) can be launched in hinges, which significantly complicates the system and makes it less reliable and more costly. It is also possible to use torsion springs placed in hinges, which, after separation from the main object and bracing of the joints, begin to swing the system into the desired position. In this case. constraints must be imposed on the generalized coordinates, which makes it necessary to install a lock in each joint in an actual construction and greatly complicates a mathematical model, due to allowance for the shock effect in each lock. The simplest and least costly in implementation and rigorous and fifirly simple in mathematical description is the launching of such a system into orbit under the influence of centrifugal forces produced as a result of its initial angular velocity in the plane perpendicular to the axes of the cylindrical hinges. For this, the space vehicle (SV) must have two devices (for example, springs) that, on command from the earth or fl'om the SV, launch the system so that, as it moves away, it begins to rotate in a given plane with respect to the SV. The mathematical description of the process of launching from an SV a system as a rigid body is fairly simple and will not be given here. If the motion of the system is considered from the moment of separation from the launchers and after bracing of the hinges, its mechanical model represents a free system of bodies connected by cylindrical hinges that accomplish

The space tethers, free or anchored, especially those proposed to equip advanced tethered low Earth orbit satellites for future space flight, experience an unusually complex behavior, and mainly doe to uncertainties in the physical constants involved. The constants for these space transportation systems are related to the properties of composite Kevlar or carbon nano-tube ribbons with length of over 20km. The mechanical properties of nano-materials are especially related to the propagation velocity of mechanical interactions, but dynamic problems are encountered from the phase of orbital deployment on. Some special case studies, under convenient assumptions, of tether deployment are presented. The non-gasdynamic, tension-free deployment is foreseen as a very economic solution and numerically simulated for twin mass systems evolving in low Earth orbits prove the feasibility of such procedures. Values of libration amplitudes in very close agreement with experimental observations are found. These tools of MLS are considered applicable to some definite configurations envisaged around the main celestial bodies of the solar system, including soft landing on celestial bodies without atmosphere. Numerical computations and dynamics simulation of free tethered satellites are demonstrated, with emphasize on the hovering of MC due to the gradient of the gravitational forces and its coupled libration.

Communications in Nonlinear Science and Numerical Simulation, 2011

The dynamics of variable-length tethers are studied using a flexible multibody dynamics method. The governing equations of the tethers are derived using a new, hybrid Eulerian and Lagrangian framework, by which the mass flow at a boundary of a tether and the length variation of a tether element are accounted for. The variable-length tether element based on the absolute nodal coordinate formulation is developed to simulate the deployment of satellite tethers. The coupled dynamic equations of tethers and satellites are obtained using the Lagrangian multiplier method. Several tethered satellite systems involving large displacements, rotations, and deformations are numerically simulated, where the tethers are released from several meters to about 1 km. A control strategy is proposed to avoid slackness of the tethers during deployment. The accuracy of the modeling and solution procedures was validated on an elevator model.

International Journal of Aerospace Engineering, 2015

The dynamics of the space tug system with a short tether similar to the ROGER system during deorbiting is presented. The kinematical characteristic of this system is significantly different from the traditional tethered system as the tether is tensional and tensionless alternately during the deorbiting process. The dynamics obtained based on the methods for the traditional tethered system is not suitable for the space tug system. Therefore, a novel method for deriving dynamics for the deorbiting system similar to the ROGER system is proposed by adopting the orbital coordinates of the two spacecraft and the Euler angles of ROGER spacecraft as the generalized coordinates instead of in- and out-plane librations and the length of the tether and so forth. Then, the librations of the system are equivalently obtained using the orbital positions of the two spacecraft. At last, the geostationary orbit (GEO) and the orbit whose apogee is 300 km above GEO are chosen as the initial and target o...

Acta Astronautica, 2010

The paper is aimed at studying the peculiarities of dynamical behavior of tether in its deployment in low Earth orbit during YES2 experiment in Foton-M3 mission, and performing flight data analysis with account of these effects. The analysis in the first part of the paper uses as input a pre-provided tension profile for the mission (resulting from a simulation to be independently validated). With this input it then performs an open-loop simulation which explains the sensitivity to the initial parameters. For the actual flight design a feedback mechanism and algorithm was used in order to control the deployment speed along a nominal profile, minimizing sensitivity to conditions such as initial velocity and endmass value.

Space tethers are cables that connect satellites or other endmasses in orbit. The emptiness of space and the near-weightlessness there make it possible to deploy very long and thin tethers. By exploiting basic principles of physics, tethers can provide propellantless propulsion and enable unique applications such as the provision of comfortable artificial gravity or the removal of space debris. Nevertheless there are still no tether applications in use today - there appears to be a "gap of scepticism". A safe tether and deployer system has therefore been designed and verified with the help of simulation and innovative ground testing equipment. Through a hands-on educational approach, the YES and YES2 low-cost space tether experiments have been launched into orbit. In September 2007, all 32 km of the YES2 tether are deployed in orbit. With the help of this tether, a student-built re-entry capsule is deorbited over Kazakhstan. This work reports this design and analysis effort, with the aim to raise confidence in the use of space tethers.

The basic results of the scientific research conducted at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (NASU) in a creative cooperation with the M. K. Yangel' SDO " Yuzhnoe " and the Institute of Technical Mechanics of NASU and the National Space Agency of Ukraine (NSAU) are generalized and systematized. The research addressed mathematical models and the dynamics of objects of space-rocket engineering such as controlled systems of rigid and elastic bodies, systems of rigid bodies of variable configuration, and systems of bodies with unilateral connections. The following information is detailed here: methods for creating spatial program motions of elastic space structures about the center of mass, methods and algorithms for mathematical simulation of the dynamics of reconfigurable spacecraft, unconventional concepts of simulating the state of weightlessness of a reconfiguring spacecraft under earth conditions on a special stand using suspension cables, different aspects of the dynamics of space cable systems, and other problems resolved within the framework of the subjects indicated. The current state of the theory of systems of rigid and deformable bodies [132, 152] is mainly determined by advances in the area of transformable space structures and robotics. Methods for constructing mathematical models of systems of solids with the topology of a tree and a closed multilink structure with up to six degrees of freedom under holonomic and nonholonomic constraints were developed in sufficient detail. The dynamics of systems of rigid and elastic bodies was extensively studied both in robotics, where individual links of the system should be considered with allowance for their deformability, and in space engineering, where spacecraft contain some elements whose deformation cannot be neglected too in solving practical problems. Modern spacecraft are, as a rule, complex structures consisting of many elements. Previously compactly packaged, such a system, once placed in an orbit, changes significantly its own configuration, which is determined by the functionality of the spacecraft. For example, solar arrays are deployed in a developed spatial structure in order to utilize maximally the radiation energy of the Sun. The bar of the gravitational stabilizer and rod antennas change from rolled ribbons into long-length elastic rods with an open cross section. Trusses replacing the bars and created from structures with a closed cross section can also carry a gravitational stabilizer, devices, etc. Large spatial antenna structures are also characteristic of the modern spacecraft. A special place in space engineering is occupied by cable systems, which can be created in the orbit from isolated bodies connected with each other and spaced several kilometers apart. Despite the great advances in the dynamics of systems of bodies, the processes described may not always be investigated within the framework of the classical dynamics of systems of rigid and even elastic bodies. The gravitational-stabilizer bar, which is a component of a reconfigurable spacecraft and is formed in the orbit from a prestressed ribbon, and the synthesized truss do not fit in the classical mathematical models of the dynamics of systems of bodies even with allowance for structural flexibility. The selection of a design model is determined in each specific case by the kinematic configuration of the system, the mechanical properties of its parts, the type of drives, and the desired accuracy of the calculations.

Acta Astronautica, 2005

The survivability analysis carried out to support the design of a new tether system, being studied in Italy for spacecraft and upper stages end-of-life de-orbiting, is presented. In particular, the problem represented by meteoroids and orbital debris impacts able to cut the tether was addressed, by considering several system conÿgurations in order to ÿnd a solution able to meet the baseline mission requirements. In addition, the not negligible collision risk with large intact space objects, and between the tethers themselves, was analysed as well in its implications.

IFAC-PapersOnLine, 2017

Discrete and Continuous Dynamical Systems - Series S, 2015

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.

This paper studies the deployment and retrieval of a tethered satellite system that is composed by two satellites connected with a flexible tether. A hybrid hinged-rod is developed based on conventional hinged-rod and bead models. The tether is discretized into rigid rods connected by springs and dampers at hinges and the end-satellites are modeled as rigid spheres. Newton-Euler method is applied to establish equations of motion for each rigid body. By adopting an instantaneity assumption and transfer mechanism between beads and rods, the proposed hybrid hinged-rod model is able to model the tether deployment and retrieval processes while avoiding the difficulty encountered due to dimension variation of rod element in deployment and retrieval. Two tethered satellite systems moving on a circular orbit with different tether lengths are investigated. Simulation results demonstrated the effectiveness and robustness of the newly developed hybrid hinged-rod model by comparing the differences between the results of the bead model and the current model with different rod element lengths.

Journal of Spacecraft and Rockets, 2007

A mechanism for control of space tether deployment is presented and discussed in this paper. This friction device called the "barberpole" was derived from the textile industry. The mechanism was analyzed, developed and tested for the second Young Engineers' Satellite mission (YES2), which is intended to feature the first European tether deployment. YES2 further aims to use the tether to accurately deorbit a small innovative re-entry capsule. The barberpole is used for precisely guiding the dynamics of a capsule by controlling the deployment velocity of a tether which connects the capsule to an orbiting platform, in this case the Foton satellite. Design steps, derivation of a mathematical model, thermal analysis and experimental results of the device are presented in this paper. The exponential dependency of applied friction force versus number of tether wraps around the pole is theoretically and experimentally proved. Friction performance and predictability are discussed based on experiments performed both on ground using a custom-built test-rig and during parabolic flight campaigns. The work highlights the suitability of the barberpole design for space tether applications.

CEAS Space Journal, 2014

Present guidelines indicate the need to deorbit new satellites launched into low Earth orbit (LEO) within 25 years from their end of life. Our research task is to develop a new technology suitable to deorbit a satellite at the end of life with as small an impact as possible on the mass budget of the mission. An alternative to the traditional chemical rockets consists in using an electrodynamic tether that, through its interaction with the Earth ionosphere and magnetic field, can take advantage of Lorentz forces for deorbiting purposes. However, Lorentz forces produce a low and yet continuous injection of energy into the system that, in the long run, can bring the tether to instability. This paper addresses this issue through the analysis of the benefits provided by an elastic-viscous damping device installed at the attachment point of the tether to the spacecraft. The analysis carried out by means of linearization of dynamics equations and numerical simulations show that a well-tuned damper can efficiently absorb the kinetic energy from the tether thus providing system stability during deorbiting.

Acta Astronautica, 1993

Abstraet-ln the first part of the paper, the divergence phenomena induced by forcing aerodynamic actions, due to orbital eccentricity and inclination to the equatorial plane, are investigated by a general, three-dimensional dynamic model of the tethered subsatellite system. In the second part, the aerodynamic stabilization of the subsatellite is considered. Although the libration mode appears almost unaffected by the passive control system, longitudinal elastic modes, with frequencies close to that of the pitch mode, can diverge for an energy transfer from the subsatellite to the tether.

This paper studies libration dynamics and stability of deorbiting nano-satellites by short and bare electrodynamic tethers. A critical aspect of satellite deorbit by an electrodynamic tether is to maintain the tether aligned with the local vertical and stable while subjected to external perturbations. The dynamics of electrodynamic tether system in deorbit application is divided into the orbital motion of the center of system’s mass and the tether libration motion relative to that center. Major space environmental perturbations including the current-induced electrodynamic force, atmospheric drag, oblateness effect of the Earth, irregularity of geomagnetic field, variable plasma density, solar radiation pressure, and lunisolar gravitational attractions are considered in the dynamic analysis. Quantitative analyses are provided in order to characterize the order of the perturbative torques during the deorbit process. A single index is derived from the libration energy to stabilize the libration motion by regulating the current in the tether through simple on-off switching. Numerical results show that the libration dynamics of an electrodynamic tether has significant impacts on the deorbit process and the electrodynamic tether cannot effectively deorbit satellites without libration stability control. The proposed current regulation strategy is simple and very effective in stabilizing libration motion of an electrodynamic tether.

Electrodynamic tether systems orbiting the Earth are prone to libration instability because of periodic changes in the geomagnetic field, plasma density, and lunisolar gravitational attractions in addition to nonperiodic changes resulting from the irregularity of the geomagnetic field, inhomogeneity of the Earth, and solar pressures. The long-term orbital and libration dynamics of a bare electrodynamic tether in deorbiting obsolete satellites is investigated by considering space environmental perturbations of current-induced electrodynamic force, atmospheric drag, Earth’s oblateness, irregularity of the geomagnetic field, variable space plasma density, solar radiation pressure, and lunisolar gravitational attractions. The electrodynamic tether is assumed to be rigid and the tethered spacecraft is modeled as a lumped mass. The study shows by numerical simulation that the out-of-plane libration is the primary source of libration instability in inclined orbits, which destabilizes the in-plane libration through nonlinear modal coupling. Accordingly, a simple stability criterion for current on/off switching control is derived from the libration energy of the tether to stabilize the out-of-plane libration by limiting the roll angle amplitude to a preset range. This in turn stabilizes the in-plane libration. The control requires only the feedback of the maximum roll angle with a minimum interval for current on/off switching imposed to avoid excessive current switching. The effectiveness of the control strategy has been demonstrated by analyzing the libration dynamics of electrodynamic tether with and without the current regulation in deorbiting satellites. Numerical results show that this approach is very effective in stabilizing both in-plane and out-of-plane libration of a tethered system subjected to periodic and nonperiodic perturbations.

Acta Mechanica, 2014

The problem of deorbiting large space debris (SLD) by means of a tethered space tug is considered. A mathematical model that describes the plane motion of the system is developed. The model takes into account the effects of the atmosphere and the rotary motion of the SLD around the SLD center of mass. The effects of the moment of tension force, gravitational moment, and pitch moment on the SLD behavior are studied. The evolution of the phase space of an angle of attack during the SLD descent is considered. Singular points are found for special cases of motion. It is shown that the effect of the atmosphere on the SLD dynamics can be neglected above an altitude of 300 km. The situation that a tether becomes slack is observed. In this case, the SLD can oscillate with increasing amplitude and even pass into rotation. This is a dangerous situation that can lead to tether rupture. A method of thrust control that provides tension in the tether during the SLD deorbiting is presented. A slack tether is also observed at atmospheric entry. This phenomenon is caused by the difference in drag forces that act on the SLD and on the space tug. The obtained results can be used in the preparation of missions of space debris deorbiting.

Journal of Physics: Conference Series, 2019

The use of innovative technologies in space missions has evolved considerably in the last decade. The use of large cables in space structures to connect spacecrafts and satellites with the goal to minimize cost of missions created a new field to be explored. A brief explanation will be considered about papers related to the equilibrium and stability of the movement of space systems connected by cables, known as Tether Systems. It will be presented the mathematical formulation for the system formed by two point masses connected by a tether in the central force field, in a Keplerian movement. The Lagrangian formulation was used to describe the rotational movement of the dumbbell-like system. Results of system behavior, tension and kinetic energy will be presented for two different situations, considering equal masses and different masses.

American Journal of Traffic and Transportation Engineering, 2019

Space tether satellites systems are one of the most promising directions in the modern space industry. Such systems consist of two or more spacecraft connected to each other by very long tethers. Great extension and variable configuration of the system in the orbital flight conditions provide some dynamic features, which are not typical of conventional spacecraft. The concept of the tethered satellite system (TSS) promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. The overarching theme of the paper is to show various control methods of the tethered satellites system (TSS) that have been undertaken recently, and also to emphasize on the importance of the TSS control method as an important aspect in the tether concepts, design, and missions. This review article presents the historical background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements. The paper introduces the strategies and methods applied in controlling the TSS not excluding their advantages and disadvantages during the tether satellite deployment, retrieval, and station keeping procedures. At the end of the paper, a conclusion is made about the effectiveness of the control methods in stabilizing the libration and vibration motions of the TSS.

Space tethers have been investigated widely as a means to provide easy access to space. However, the design and construction of such a device presents significant unsolved technological challenges. We propose an alternative approach to the construction of a space elevator that utilizes a free-standing core structure to provide access to near space regions and to reduce the cost of space launch. The structure is comprised of pneumatically inflated sections that are actively controlled and stabilized to balance external disturbances and support the structure. Such an approach avoids problems associated with a space tether including material strength constraints, the need for in-space construction, the fabrication of a cable at least 50,000 km in length, and the ageing and meteorite-damage effects associated with a thin tether or cable in Low Earth Orbit. An example structure constructed at 5 km altitude and extending to 20 km above sea level is described. The stability and control of the structure, methods for construction and its utility for space launch and other applications are discussed.