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Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid
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Dynamics of a tethered satellite with variable mass
1. | National Research Institute of Astronomy and Geophysics, Cairo, Egypt |
2. | Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena, Región de Murcia |
3. | Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia, Saudi Arabia |
References:
[1] |
E. I. Abouelmagd, J. L. G. Guirao and J. A. Vera, Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body, Communications in Nonlinear Science and Numerical Simulation, 20 (2015), 1057-1069.
doi: 10.1016/j.cnsns.2014.06.033. |
[2] |
F. Austin, Nonlinear dynamics of free-rotating flexibly connected double-mass space station, Journal of Spacecraft and Rockets, 2 (1965), 901-906. |
[3] |
G. Avanzini and M. Fedi, Effects of eccentricity of the reference orbit on multi-tethered satellite formations, Acta Astronautica, 94 (2014), 338-350.
doi: 10.1016/j.actaastro.2013.03.019. |
[4] |
V. V. Beletsky and E. M. Levin, Dynamics of Space Tether Systems, Univelt, San Diego, 1993. |
[5] |
V. V. Beletsky, Motion of an Artificial Satellite about its Center of Mass, Israel Program for Scientific Translations, Jerusalem, 1966. |
[6] |
A. Burov and A. Dugain, Planar oscillations of a vibrating dumbbell-like body in a central field of forces, Cosmic Research, 49 (2011), 353-359.
doi: 10.1134/S0010952511040010. |
[7] |
A. Burov, I. I. Kosenko and H. Troger, On periodic motions of an orbital dumbbell-shaped body with a cabin-elevator, Mechanics of Solids, 47 (2012), 269-284.
doi: 10.3103/S0025654412030028. |
[8] |
A. Celletti and V. Sidorenko, Some properties of the dumbbell satellite attitude dynamics, Celest. Mech. Dyn. Astr., 101 (2008), 105-126.
doi: 10.1007/s10569-008-9122-0. |
[9] |
V. Chobotov, Gravitational excitation of extensible dumbbell satellite, Journal of Spacecraft and Rockets, 4 (1967), 1295-1300.
doi: 10.2514/3.29074. |
[10] |
G. Colombo, E. M. Gaposchkin, M. D. Grossi and G. C. Weiffenbach, The skyhook: A shuttle-borne tool for low-orbital-altitude research, Meccanica, 10 (1975), 3-20.
doi: 10.1007/BF02148280. |
[11] |
M. L. Cosmo and E. C. Lorenzini, Tethers in Space Handbook, 3rd Ed., NASA Marshall Space Flight Center, Huntsville, 1997. |
[12] |
L. Gang, H. Jing, M. Guangfu and L. Chuanjiang, Nonlinear dynamics and station keeping control of a rotating tethered satellite system in halo orbits, Chinese Journal of Aeronautics, 26 (2013), 1227-1237. |
[13] |
J. L. G. Guirao, J. A. Vera and B. A. Wade, On the periodic solutions of a rigid dumbbell satellite in a circular orbit, Astrophys Space Sci, 346 (2013), 437-442.
doi: 10.1007/s10509-013-1456-8. |
[14] |
F. C. Hurlbut and J. L. Potter, Tethered aerothermodynamic research needs, Journal of Spacecraft and Rockets, 28 (1991), 50-57.
doi: 10.2514/6.1990-533. |
[15] |
S. K. Jha and A. K. Shrivastava, Equations of motion of the elliptical restricted problem of three bodies with variable masses, The Astronomical Journal, 121 (2001), 580-583.
doi: 10.1086/318006. |
[16] |
A. J. Maciejewski, M. Przybylska, L. Simpson and W. Szumiński, Non-integrability of the dumbbell and point mass problem, Celest. Mech. Dyn. Astr., 117 (2013), 315-330.
doi: 10.1007/s10569-013-9514-7. |
[17] |
I. V. Meshcherskii, Works on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1952. |
[18] |
M. A. Munitsina, Relative equilibrium on the circular Keplerian orbit of the "Dumbbells-Load'' system with unilateral connections, Automation and Remote Control, 68 (2007), 1476-1481.
doi: 10.1134/S0005117907090020. |
[19] |
K. Nakanishi, H. Kojima and T. Watanabe, Trajectories of in-plane periodic solutions of tethered satellite system projected on van der Pol planes, Acta Astronautica, 68 (2011), 1024-1030.
doi: 10.1016/j.actaastro.2010.09.014. |
[20] |
D. D. Nixon, Dynamics of a spinning space station with a counterweight connected by multiple cables, Journal of Spacecraft and Rockets, 9 (1972), 896-902.
doi: 10.2514/6.1972-172. |
[21] |
M. Pasca and E. Lorenzini, Collection of martian atmospheric dust with a low altitude tethered probe, in Spaceflight Mechanics 1991; Proceedings of the 1st AAS/AIAA Annual Spaceflight Mechanics Meeting, Houston, TX, 1991, 1121-1139. |
[22] |
C. D. Pengelley, Preliminary survey of dynamic stability of cable-connected spinning space station, Journal of Spacecraft and Rockets, 3 (1966), 1456-1462.
doi: 10.2514/3.28677. |
[23] |
K. A. Polzin, E. Y. Choueiri, P. Gurfil and N. J. Kasdin, Plasma propulsion options for multiple terrestrial planet finder architectures, Journal of Spacecraft and Rockets, 39 (2002), 347-356.
doi: 10.2514/2.3833. |
[24] |
M. B. Quadrelli, Dynamics and control of novel orbiting formations with internal dynamics, Journal of the Astronautical Sciences, 51 (2003), 319-337. |
[25] |
B. Wong and A. Misra, Planar dynamics of variable length multi-tethered spacecraft near collinear Lagrangian points, Acta Astronautica, 63 (2008), 1178-1187.
doi: 10.1016/j.actaastro.2008.06.022. |
[26] |
W. Zhang, F. B. Gao and M. H. Yao, Periodic solutions and stability of a tethered satellite system, Mechanics Research Communications, 44 (2012), 24-29.
doi: 10.1016/j.mechrescom.2012.05.004. |
show all references
References:
[1] |
E. I. Abouelmagd, J. L. G. Guirao and J. A. Vera, Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body, Communications in Nonlinear Science and Numerical Simulation, 20 (2015), 1057-1069.
doi: 10.1016/j.cnsns.2014.06.033. |
[2] |
F. Austin, Nonlinear dynamics of free-rotating flexibly connected double-mass space station, Journal of Spacecraft and Rockets, 2 (1965), 901-906. |
[3] |
G. Avanzini and M. Fedi, Effects of eccentricity of the reference orbit on multi-tethered satellite formations, Acta Astronautica, 94 (2014), 338-350.
doi: 10.1016/j.actaastro.2013.03.019. |
[4] |
V. V. Beletsky and E. M. Levin, Dynamics of Space Tether Systems, Univelt, San Diego, 1993. |
[5] |
V. V. Beletsky, Motion of an Artificial Satellite about its Center of Mass, Israel Program for Scientific Translations, Jerusalem, 1966. |
[6] |
A. Burov and A. Dugain, Planar oscillations of a vibrating dumbbell-like body in a central field of forces, Cosmic Research, 49 (2011), 353-359.
doi: 10.1134/S0010952511040010. |
[7] |
A. Burov, I. I. Kosenko and H. Troger, On periodic motions of an orbital dumbbell-shaped body with a cabin-elevator, Mechanics of Solids, 47 (2012), 269-284.
doi: 10.3103/S0025654412030028. |
[8] |
A. Celletti and V. Sidorenko, Some properties of the dumbbell satellite attitude dynamics, Celest. Mech. Dyn. Astr., 101 (2008), 105-126.
doi: 10.1007/s10569-008-9122-0. |
[9] |
V. Chobotov, Gravitational excitation of extensible dumbbell satellite, Journal of Spacecraft and Rockets, 4 (1967), 1295-1300.
doi: 10.2514/3.29074. |
[10] |
G. Colombo, E. M. Gaposchkin, M. D. Grossi and G. C. Weiffenbach, The skyhook: A shuttle-borne tool for low-orbital-altitude research, Meccanica, 10 (1975), 3-20.
doi: 10.1007/BF02148280. |
[11] |
M. L. Cosmo and E. C. Lorenzini, Tethers in Space Handbook, 3rd Ed., NASA Marshall Space Flight Center, Huntsville, 1997. |
[12] |
L. Gang, H. Jing, M. Guangfu and L. Chuanjiang, Nonlinear dynamics and station keeping control of a rotating tethered satellite system in halo orbits, Chinese Journal of Aeronautics, 26 (2013), 1227-1237. |
[13] |
J. L. G. Guirao, J. A. Vera and B. A. Wade, On the periodic solutions of a rigid dumbbell satellite in a circular orbit, Astrophys Space Sci, 346 (2013), 437-442.
doi: 10.1007/s10509-013-1456-8. |
[14] |
F. C. Hurlbut and J. L. Potter, Tethered aerothermodynamic research needs, Journal of Spacecraft and Rockets, 28 (1991), 50-57.
doi: 10.2514/6.1990-533. |
[15] |
S. K. Jha and A. K. Shrivastava, Equations of motion of the elliptical restricted problem of three bodies with variable masses, The Astronomical Journal, 121 (2001), 580-583.
doi: 10.1086/318006. |
[16] |
A. J. Maciejewski, M. Przybylska, L. Simpson and W. Szumiński, Non-integrability of the dumbbell and point mass problem, Celest. Mech. Dyn. Astr., 117 (2013), 315-330.
doi: 10.1007/s10569-013-9514-7. |
[17] |
I. V. Meshcherskii, Works on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1952. |
[18] |
M. A. Munitsina, Relative equilibrium on the circular Keplerian orbit of the "Dumbbells-Load'' system with unilateral connections, Automation and Remote Control, 68 (2007), 1476-1481.
doi: 10.1134/S0005117907090020. |
[19] |
K. Nakanishi, H. Kojima and T. Watanabe, Trajectories of in-plane periodic solutions of tethered satellite system projected on van der Pol planes, Acta Astronautica, 68 (2011), 1024-1030.
doi: 10.1016/j.actaastro.2010.09.014. |
[20] |
D. D. Nixon, Dynamics of a spinning space station with a counterweight connected by multiple cables, Journal of Spacecraft and Rockets, 9 (1972), 896-902.
doi: 10.2514/6.1972-172. |
[21] |
M. Pasca and E. Lorenzini, Collection of martian atmospheric dust with a low altitude tethered probe, in Spaceflight Mechanics 1991; Proceedings of the 1st AAS/AIAA Annual Spaceflight Mechanics Meeting, Houston, TX, 1991, 1121-1139. |
[22] |
C. D. Pengelley, Preliminary survey of dynamic stability of cable-connected spinning space station, Journal of Spacecraft and Rockets, 3 (1966), 1456-1462.
doi: 10.2514/3.28677. |
[23] |
K. A. Polzin, E. Y. Choueiri, P. Gurfil and N. J. Kasdin, Plasma propulsion options for multiple terrestrial planet finder architectures, Journal of Spacecraft and Rockets, 39 (2002), 347-356.
doi: 10.2514/2.3833. |
[24] |
M. B. Quadrelli, Dynamics and control of novel orbiting formations with internal dynamics, Journal of the Astronautical Sciences, 51 (2003), 319-337. |
[25] |
B. Wong and A. Misra, Planar dynamics of variable length multi-tethered spacecraft near collinear Lagrangian points, Acta Astronautica, 63 (2008), 1178-1187.
doi: 10.1016/j.actaastro.2008.06.022. |
[26] |
W. Zhang, F. B. Gao and M. H. Yao, Periodic solutions and stability of a tethered satellite system, Mechanics Research Communications, 44 (2012), 24-29.
doi: 10.1016/j.mechrescom.2012.05.004. |
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