Résumé/Abstract Previously a new dynamic instability that affected electrodynamic tethers in incl... more Résumé/Abstract Previously a new dynamic instability that affected electrodynamic tethers in inclined orbits was studied, with a simple one-bar model that neglected the contribution of the tether lateral dynamics. The flexibility of the tether (lateral dynamics), however, plays ...
Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential prof... more Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential profile along a passive bare electrodynamic tether is provided using perturbation theory. An ad hoc nondimensional formulation of the governing local bias and orbital motion limited ...
A linear analysis of the attitude dynamics of a flexible electrodynamic tether is carried out. Th... more A linear analysis of the attitude dynamics of a flexible electrodynamic tether is carried out. The conductive tether is considered insulated and the current is collected by a terminating balloon. Both the libration and lateral oscillations are considered, and these last are expanded in normal modes. Without the electrodynamic forces, the oscillations pertaining to orthogonal planes are completely uncoupled, and the temporal scale of the librations is quite different from the temporal scale of the lateral modes. Thus, it is possible to study separately the librations from the lateral dynamics by averaging on time. However, the electrodynamic forces cause the coupling of all the oscillations. It is no longer possible to analyze the librations separately from the lateral modes, since these last acquire frequencies of the same order of those of the librations. It is well known that electrodynainic tethers working at inclined orbits exhibit dynamic instabilities. Within the linear analys...
Se analiza la dinámica de amarras espaciales electrodinámicas en órbita inclinada. Su actitud pre... more Se analiza la dinámica de amarras espaciales electrodinámicas en órbita inclinada. Su actitud presenta inestabilidades a largo plazo, en ausencia de amortiguamiento o control. No obstante, la inestabilidad desaparece, o se reduce drásticamente, cuando la amarra está auto equilibrada, esto es, cuando se anula el par de Lorentz alrededor del centro de masas del sistema. En este artículo se describen con detalle los principales parámetros involucrados en la dinámica de la amarra, y su influencia sobre la condición de auto equilibrado. El estudio, restringido al régimen generador, puede extenderse sin dificultad al régimen motor. Se propone, además, una estrategia para manetener la amarra equilibrada teniendo en cuenta, en su totalidad, la trayectoria seguida por el sistema durante la fase de descenso. La estrategia puede implementarse de forma simple y permite aumnetar la controlabilidad del sistema.
Resumen Las amarras electrodinámicas auto-equilibradas (SBET, en siglas anglosajonas) pueden de-o... more Resumen Las amarras electrodinámicas auto-equilibradas (SBET, en siglas anglosajonas) pueden de-orbitar objetos e orbitas bajas terrestres (LEO). Aproximadamente, el 98 % de la basura espacial se concentra en 1500 masas de más de 100 kg. De-orbitar alguno de esos objetos disminuiría de forma considerable la población de basura espacial. Las amarras electrodinámicas (ET, en siglas inglesas) son capaces de ejercer resistencia electrodinámica en alturas donde la resistencia aerodinámica es despreciable (p.ej., 2000 km). Esta generación de resistencia es fiable, más económica que otras soluciones y permite de-orbitar satélites al final de su vidá util, así como otros deshechos espaciales. Los ET no utilizan propulsante para llevar a cabo su misión; antes al contrario, pueden recuperar una parte significativa de la energía orbital de la basura espacial de-orbitada durante el proceso, si esta opción se considera aconsejable. Estas ven-tajas de las amarras electrodinámicas hacen que, proba...
ABSTRACT The generator regime of electrodynamic bare tethers working at inclined orbits is analyz... more ABSTRACT The generator regime of electrodynamic bare tethers working at inclined orbits is analyzed. Without damping or some kind of control, the attitude dynamics of these tethers is unstable. However, the instability disappears, or reduces drastically, when the tether is self-balanced, that is, when the Lorentz torque about the system center of mass,vanishes. The aim of the paper is to describe in detail the main parameters involved in the dynamics of this type of tether and also their influence on the balance condition. In addition, a strategy will be proposed to keep the. tether balanced, taking into account the whole trajectory followed by the system during the deorbiting process.
Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential prof... more Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential profile along a passive bare electrodynamic tether is provided using perturbation theory. An ad hoc nondimensional formulation of the governing local bias and orbital motion limited ...
ABSTRACT It is well known that an electrodynamic tether exhibits dynamic instabilities. A mathema... more ABSTRACT It is well known that an electrodynamic tether exhibits dynamic instabilities. A mathematical model of the system under some simplifying assumptions is developed. An inextensible wire with two point end masses in a circular orbit is considered; the conductor is insulated from the ambient plasma. The system attitude dynamics is analyzed within a linear approximation, and the tether lateral oscillations are expanded in normal modes. It is found that the electrodynamic forces cause the coupling of all cable oscillations. The lateral modes acquire frequencies of the same order of magnitude as the frequencies of the librations. At a nonnull inclination, a source of instability is found to be associated to a mechanism of classical, resonance between the out-of-plane libration and the electrodynamic forcing terms. Because of their coupling with the librations, the lateral modes are also destabilized, with odd lateral modes more excited than the even ones. The geomagnetic field and the tether current have Fourier spectra rich in frequencies, and this makes the start of instability easier.
Recent gravity field determination missions have shown the possibility of improving our Earth kno... more Recent gravity field determination missions have shown the possibility of improving our Earth knowledge from space. GRACE has helped to the determination of temporal variations of low and mean degrees of the field while GOCE will improve the precision in the determination of higher degrees. But there is still some needs for geophysics which are not satisfied by these missions. Two areas where improvements must be done are (i) perenniality of the observations, and (ii) determination of temporal variations of higher degrees of the gravity field. These improvements can be achieved thanks to new measurement technologies with higher precision, but also using new observables. Historically, space determination of the gravity field has been done observing the perturbations of the orbit of the satellites. More recently, GRACE has introduced the use of satellite-tosatellite ranging. Goce will use onboard gradiometry. The authors have explored the possibilities of two new technologies for the determination of the gravity field: (i) tethered systems, and (ii) formation flying for all kind of configurations (not just leader-follower). To analyze the possibilities of these technologies, we obtain the covariance matrix of the coefficients of the gravity field for the different observables. This can be done providing some very reasonable hypothesis are accepted. This matrix contains a lot of information concerning the behavior of the observable. In order to obtain the matrix, we use the so-called lumped coefficients approach. We have used this method for three observables (i) tethered systems, (ii) formation flying and (iii) gradiometry (for comparison purposes). Tethers appear as a very long base gradiometers, with very interesting properties, but also very challenging from a technological point of view. One of the major advantages of the tethered systems is their multitask design. Indeed, the same cable can be used for propulsion purposes in some phases of the mission, and for geodesy purposes in other phases. Several studies have been presented using formation flying, but none of them is exhaustive in terms of number of satellites, configuration, and plan of the motion. We study formation flying using differential orbital elements in order to be as general as possible. The advantage of this representation is the possibility to study all sort of initial conditions and reference orbits with a posterior analysis of covariance matrices. Our results show the intrinsic possibilities of these new two systems and their comparison with existing ones. We also define some baseline scenarios for future missions.
... Authors: Peláez Alvarez, J.; Lorenzini, EC. Publication: Proceedings of the Fourth Internatio... more ... Authors: Peláez Alvarez, J.; Lorenzini, EC. Publication: Proceedings of the Fourth International Conference on Tethers in Space, pp. 563-576, 10-14 April 1995, Smithsonian Institution, Washington, DC., p.563. Publication Date: 04/1995. Origin: AUTHOR. ...
Résumé/Abstract Previously a new dynamic instability that affected electrodynamic tethers in incl... more Résumé/Abstract Previously a new dynamic instability that affected electrodynamic tethers in inclined orbits was studied, with a simple one-bar model that neglected the contribution of the tether lateral dynamics. The flexibility of the tether (lateral dynamics), however, plays ...
Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential prof... more Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential profile along a passive bare electrodynamic tether is provided using perturbation theory. An ad hoc nondimensional formulation of the governing local bias and orbital motion limited ...
A linear analysis of the attitude dynamics of a flexible electrodynamic tether is carried out. Th... more A linear analysis of the attitude dynamics of a flexible electrodynamic tether is carried out. The conductive tether is considered insulated and the current is collected by a terminating balloon. Both the libration and lateral oscillations are considered, and these last are expanded in normal modes. Without the electrodynamic forces, the oscillations pertaining to orthogonal planes are completely uncoupled, and the temporal scale of the librations is quite different from the temporal scale of the lateral modes. Thus, it is possible to study separately the librations from the lateral dynamics by averaging on time. However, the electrodynamic forces cause the coupling of all the oscillations. It is no longer possible to analyze the librations separately from the lateral modes, since these last acquire frequencies of the same order of those of the librations. It is well known that electrodynainic tethers working at inclined orbits exhibit dynamic instabilities. Within the linear analys...
Se analiza la dinámica de amarras espaciales electrodinámicas en órbita inclinada. Su actitud pre... more Se analiza la dinámica de amarras espaciales electrodinámicas en órbita inclinada. Su actitud presenta inestabilidades a largo plazo, en ausencia de amortiguamiento o control. No obstante, la inestabilidad desaparece, o se reduce drásticamente, cuando la amarra está auto equilibrada, esto es, cuando se anula el par de Lorentz alrededor del centro de masas del sistema. En este artículo se describen con detalle los principales parámetros involucrados en la dinámica de la amarra, y su influencia sobre la condición de auto equilibrado. El estudio, restringido al régimen generador, puede extenderse sin dificultad al régimen motor. Se propone, además, una estrategia para manetener la amarra equilibrada teniendo en cuenta, en su totalidad, la trayectoria seguida por el sistema durante la fase de descenso. La estrategia puede implementarse de forma simple y permite aumnetar la controlabilidad del sistema.
Resumen Las amarras electrodinámicas auto-equilibradas (SBET, en siglas anglosajonas) pueden de-o... more Resumen Las amarras electrodinámicas auto-equilibradas (SBET, en siglas anglosajonas) pueden de-orbitar objetos e orbitas bajas terrestres (LEO). Aproximadamente, el 98 % de la basura espacial se concentra en 1500 masas de más de 100 kg. De-orbitar alguno de esos objetos disminuiría de forma considerable la población de basura espacial. Las amarras electrodinámicas (ET, en siglas inglesas) son capaces de ejercer resistencia electrodinámica en alturas donde la resistencia aerodinámica es despreciable (p.ej., 2000 km). Esta generación de resistencia es fiable, más económica que otras soluciones y permite de-orbitar satélites al final de su vidá util, así como otros deshechos espaciales. Los ET no utilizan propulsante para llevar a cabo su misión; antes al contrario, pueden recuperar una parte significativa de la energía orbital de la basura espacial de-orbitada durante el proceso, si esta opción se considera aconsejable. Estas ven-tajas de las amarras electrodinámicas hacen que, proba...
ABSTRACT The generator regime of electrodynamic bare tethers working at inclined orbits is analyz... more ABSTRACT The generator regime of electrodynamic bare tethers working at inclined orbits is analyzed. Without damping or some kind of control, the attitude dynamics of these tethers is unstable. However, the instability disappears, or reduces drastically, when the tether is self-balanced, that is, when the Lorentz torque about the system center of mass,vanishes. The aim of the paper is to describe in detail the main parameters involved in the dynamics of this type of tether and also their influence on the balance condition. In addition, a strategy will be proposed to keep the. tether balanced, taking into account the whole trajectory followed by the system during the deorbiting process.
Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential prof... more Résumé/Abstract A relatively high-accuracy analytical solution for the current and potential profile along a passive bare electrodynamic tether is provided using perturbation theory. An ad hoc nondimensional formulation of the governing local bias and orbital motion limited ...
ABSTRACT It is well known that an electrodynamic tether exhibits dynamic instabilities. A mathema... more ABSTRACT It is well known that an electrodynamic tether exhibits dynamic instabilities. A mathematical model of the system under some simplifying assumptions is developed. An inextensible wire with two point end masses in a circular orbit is considered; the conductor is insulated from the ambient plasma. The system attitude dynamics is analyzed within a linear approximation, and the tether lateral oscillations are expanded in normal modes. It is found that the electrodynamic forces cause the coupling of all cable oscillations. The lateral modes acquire frequencies of the same order of magnitude as the frequencies of the librations. At a nonnull inclination, a source of instability is found to be associated to a mechanism of classical, resonance between the out-of-plane libration and the electrodynamic forcing terms. Because of their coupling with the librations, the lateral modes are also destabilized, with odd lateral modes more excited than the even ones. The geomagnetic field and the tether current have Fourier spectra rich in frequencies, and this makes the start of instability easier.
Recent gravity field determination missions have shown the possibility of improving our Earth kno... more Recent gravity field determination missions have shown the possibility of improving our Earth knowledge from space. GRACE has helped to the determination of temporal variations of low and mean degrees of the field while GOCE will improve the precision in the determination of higher degrees. But there is still some needs for geophysics which are not satisfied by these missions. Two areas where improvements must be done are (i) perenniality of the observations, and (ii) determination of temporal variations of higher degrees of the gravity field. These improvements can be achieved thanks to new measurement technologies with higher precision, but also using new observables. Historically, space determination of the gravity field has been done observing the perturbations of the orbit of the satellites. More recently, GRACE has introduced the use of satellite-tosatellite ranging. Goce will use onboard gradiometry. The authors have explored the possibilities of two new technologies for the determination of the gravity field: (i) tethered systems, and (ii) formation flying for all kind of configurations (not just leader-follower). To analyze the possibilities of these technologies, we obtain the covariance matrix of the coefficients of the gravity field for the different observables. This can be done providing some very reasonable hypothesis are accepted. This matrix contains a lot of information concerning the behavior of the observable. In order to obtain the matrix, we use the so-called lumped coefficients approach. We have used this method for three observables (i) tethered systems, (ii) formation flying and (iii) gradiometry (for comparison purposes). Tethers appear as a very long base gradiometers, with very interesting properties, but also very challenging from a technological point of view. One of the major advantages of the tethered systems is their multitask design. Indeed, the same cable can be used for propulsion purposes in some phases of the mission, and for geodesy purposes in other phases. Several studies have been presented using formation flying, but none of them is exhaustive in terms of number of satellites, configuration, and plan of the motion. We study formation flying using differential orbital elements in order to be as general as possible. The advantage of this representation is the possibility to study all sort of initial conditions and reference orbits with a posterior analysis of covariance matrices. Our results show the intrinsic possibilities of these new two systems and their comparison with existing ones. We also define some baseline scenarios for future missions.
... Authors: Peláez Alvarez, J.; Lorenzini, EC. Publication: Proceedings of the Fourth Internatio... more ... Authors: Peláez Alvarez, J.; Lorenzini, EC. Publication: Proceedings of the Fourth International Conference on Tethers in Space, pp. 563-576, 10-14 April 1995, Smithsonian Institution, Washington, DC., p.563. Publication Date: 04/1995. Origin: AUTHOR. ...
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