-
Previous Article
Reproducing kernel functions for difference equations
- DCDS-S Home
- This Issue
-
Next Article
Dynamics of a tethered satellite with variable mass
Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid
1. | National Research Institute of Astronomy and Geophysics, Cairo |
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 |
References:
[1] |
E. I. Abouelmagd, Existence and stability of triangular points in the restricted three-body problem with numerical applications, Astrophysics and Space Science, 342 (2012), 45-53.
doi: 10.1007/s10509-012-1162-y. |
[2] |
E. I. Abouelmagd, M. E. Awad, E. M. A. Elzayat and I. A. Abbas, Reduction the secular solution to periodic solution in the generalized restricted three-body problem, Astrophysics and Space Science, 350 (2014), 495-505.
doi: 10.1007/s10509-013-1756-z. |
[3] |
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, Commun. Nonlinear Sci. Numer Simulation, 20 (2015), 1057-1069.
doi: 10.1016/j.cnsns.2014.06.033. |
[4] |
E. I. Abouelmagd, M. C. Alhothuali, J. L. G. Guirao and H. M. Malaikah, The effect of zonal harmonic coefficients in the framework of the restricted three朾ody problem, Advances in Space Research, 55 (2015), 1660-1672.
doi: 10.1016/j.asr.2014.12.030. |
[5] |
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. |
[6] |
A. 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. |
[7] |
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. |
[8] |
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. |
[9] |
J. A. Vera, On the periodic solutions of a rigid dumbbell satellite placed at L4 of the restricted three body problem, International Journal of Non-Linear Mechanics, 51 (2013), 152-156.
doi: 10.1016/j.ijnonlinmec.2013.01.013. |
[10] |
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. |
[11] |
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, Existence and stability of triangular points in the restricted three-body problem with numerical applications, Astrophysics and Space Science, 342 (2012), 45-53.
doi: 10.1007/s10509-012-1162-y. |
[2] |
E. I. Abouelmagd, M. E. Awad, E. M. A. Elzayat and I. A. Abbas, Reduction the secular solution to periodic solution in the generalized restricted three-body problem, Astrophysics and Space Science, 350 (2014), 495-505.
doi: 10.1007/s10509-013-1756-z. |
[3] |
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, Commun. Nonlinear Sci. Numer Simulation, 20 (2015), 1057-1069.
doi: 10.1016/j.cnsns.2014.06.033. |
[4] |
E. I. Abouelmagd, M. C. Alhothuali, J. L. G. Guirao and H. M. Malaikah, The effect of zonal harmonic coefficients in the framework of the restricted three朾ody problem, Advances in Space Research, 55 (2015), 1660-1672.
doi: 10.1016/j.asr.2014.12.030. |
[5] |
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. |
[6] |
A. 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. |
[7] |
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. |
[8] |
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. |
[9] |
J. A. Vera, On the periodic solutions of a rigid dumbbell satellite placed at L4 of the restricted three body problem, International Journal of Non-Linear Mechanics, 51 (2013), 152-156.
doi: 10.1016/j.ijnonlinmec.2013.01.013. |
[10] |
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. |
[11] |
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. |
[1] |
Jifeng Chu, Zaitao Liang, Pedro J. Torres, Zhe Zhou. Existence and stability of periodic oscillations of a rigid dumbbell satellite around its center of mass. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2669-2685. doi: 10.3934/dcdsb.2017130 |
[2] |
Frederic Laurent-Polz, James Montaldi, Mark Roberts. Point vortices on the sphere: Stability of symmetric relative equilibria. Journal of Geometric Mechanics, 2011, 3 (4) : 439-486. doi: 10.3934/jgm.2011.3.439 |
[3] |
Lyudmila Grigoryeva, Juan-Pablo Ortega, Stanislav S. Zub. Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies. Journal of Geometric Mechanics, 2014, 6 (3) : 373-415. doi: 10.3934/jgm.2014.6.373 |
[4] |
James Montaldi. Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry. Journal of Geometric Mechanics, 2014, 6 (2) : 237-260. doi: 10.3934/jgm.2014.6.237 |
[5] |
Miguel Rodríguez-Olmos. Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy. Journal of Geometric Mechanics, 2020, 12 (3) : 525-540. doi: 10.3934/jgm.2020019 |
[6] |
David Rojas, Pedro J. Torres. Bifurcation of relative equilibria generated by a circular vortex path in a circular domain. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 749-760. doi: 10.3934/dcdsb.2019265 |
[7] |
Alain Albouy, Holger R. Dullin. Relative equilibria of the 3-body problem in $ \mathbb{R}^4 $. Journal of Geometric Mechanics, 2020, 12 (3) : 323-341. doi: 10.3934/jgm.2020012 |
[8] |
Marshall Hampton, Anders Nedergaard Jensen. Finiteness of relative equilibria in the planar generalized $N$-body problem with fixed subconfigurations. Journal of Geometric Mechanics, 2015, 7 (1) : 35-42. doi: 10.3934/jgm.2015.7.35 |
[9] |
Florian Rupp, Jürgen Scheurle. Classification of a class of relative equilibria in three body coulomb systems. Conference Publications, 2011, 2011 (Special) : 1254-1262. doi: 10.3934/proc.2011.2011.1254 |
[10] |
Christine Bachoc, Gilles Zémor. Bounds for binary codes relative to pseudo-distances of $k$ points. Advances in Mathematics of Communications, 2010, 4 (4) : 547-565. doi: 10.3934/amc.2010.4.547 |
[11] |
PaweŁ Hitczenko, Georgi S. Medvedev. Stability of equilibria of randomly perturbed maps. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 369-381. doi: 10.3934/dcdsb.2017017 |
[12] |
D. J. W. Simpson. On the stability of boundary equilibria in Filippov systems. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3093-3111. doi: 10.3934/cpaa.2021097 |
[13] |
Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences & Engineering, 2016, 13 (1) : 101-118. doi: 10.3934/mbe.2016.13.101 |
[14] |
Jifa Jiang, Lei Niu. On the equivalent classification of three-dimensional competitive Atkinson/Allen models relative to the boundary fixed points. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 217-244. doi: 10.3934/dcds.2016.36.217 |
[15] |
Denis Serre, Alexis F. Vasseur. The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4569-4577. doi: 10.3934/dcds.2016.36.4569 |
[16] |
Dieter Schmidt, Lucas Valeriano. Nonlinear stability of stationary points in the problem of Robe. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1917-1936. doi: 10.3934/dcdsb.2016029 |
[17] |
Sílvia Cuadrado. Stability of equilibria of a predator-prey model of phenotype evolution. Mathematical Biosciences & Engineering, 2009, 6 (4) : 701-718. doi: 10.3934/mbe.2009.6.701 |
[18] |
Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567 |
[19] |
William H. Sandholm. Local stability of strict equilibria under evolutionary game dynamics. Journal of Dynamics and Games, 2014, 1 (3) : 485-495. doi: 10.3934/jdg.2014.1.485 |
[20] |
Yacine Chitour, Frédéric Grognard, Georges Bastin. Equilibria and stability analysis of a branched metabolic network with feedback inhibition. Networks and Heterogeneous Media, 2006, 1 (1) : 219-239. doi: 10.3934/nhm.2006.1.219 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]