Fetching the paper…
Reading the bibliography…
The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites.
C. Folkestad, D. Pastor, I. Mezic, R. Mohr, M. Fonoberova, J. Burdick, Extended dynamic mode decomposition with learned koopman eigenfunctions for prediction and control (2020) · 1911
Earlier work this paper cites.
arXiv:https://www.pnas.org/doi/pdf/10.1073/pnas.17.5.315
B. O. Koopman, Hamiltonian systems and transformation in hilbert space , Proceedings of the National Academy of Sciences 17 (5) (1931) 315–318 · 1931
Earlier work this paper cites.
doi:10.1061/(ASCE)SU.1943-5428.0000382
A. Allahvirdi-Zadeh, K. Wang, A. El-Mowafy, Precise orbit determination of leo satellites based on undifferenced gnss observations , Journal of Surveying Engineering 148 (1) (2022) 03121001 · 1943
Earlier work this paper cites.
doi:10.1017/S0305004100030401
R. Penrose, A generalized inverse for matrices, Mathematical Proceedings of the Cambridge Philosophical Society 51 (3) (1955) 406–413 · 1955
Earlier work this paper cites.
W. H. CLOHESSY, R. S. WILTSHIRE, Terminal guidance system for satellite rendezvous. , Journal of the Aerospace Sciences 27 (9) (1960) 653 – 658. URL https://arc.aiaa.org/doi/abs/10.2514/8.8704
1960
Earlier work this paper cites.
V. Szebehely, Theory of Orbit: The Restricted Problem of Three Bodies, Academic Press, New York, NY, 1967
1967
Earlier work this paper cites.
L. Meirovitch, Methods of Analytical Dynamics , Advanced engineering series, McGraw-Hill, 1970. URL https://books.google.com/books?id=GlV5ywEACAAJ
1970
Earlier work this paper cites.
G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems 2 (4) (1989) 303–314
1989
Earlier work this paper cites.
K. Hornik, M. Stinchcombe, H. White, Multilayer feedforward networks are universal approximators, Neural networks 2 (5) (1989) 359–366
1989
Earlier work this paper cites.
C. Marchal, The three-body problem, no. 4 in Studies in Astronautics, Elsevier, Amsterdam, Netherlands, 1990
1990
Earlier work this paper cites.
K. Hornik, M. Stinchcombe, H. White, Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks, Neural networks 3 (5) (1990) 551–560
1990
Earlier work this paper cites.
J. Barrow-Green, Poincaré and the three body problem, AMS, Providence, RI, 1997
1997
Earlier work this paper cites.
D. Vallado, W. McClain, Fundamentals of Astrodynamics and Applications , College custom series, McGraw-Hill Companies, Incorporated, 1997. URL https://books.google.com/books?id=pGqFPwAACAAJ
1997
Earlier work this paper cites.
doi:10.1103/RevModPhys.70.589
M. C. Gutzwiller, Moon-Earth-Sun: The oldest three-body problem, Rev. Mod. Phys. 70 (2) (1998) 589–639 · 1998
Earlier work this paper cites.
C. D. Murray, S. F. Dermott, Solar System Dynamics, Cambridge Univ. Press, Cambridge, UK, 1999
1999
Earlier work this paper cites.
R. Battin, An Introduction to the Mathematics and Methods of Astrodynamics , AIAA Education Series, American Institute of Aeronautics & Astronautics, 1999. URL https://books.google.com/books?id=OjH7aVhiGdcC
1999
Earlier work this paper cites.
S. J. Aarseth, Gravitational N-Body Simulations, Cambridge: Cambridge University Press, 2003
2003
Earlier work this paper cites.
doi:10.1145/1015330.1015435
A. Y. Ng, Feature selection, l1 vs. l2 regularization, and rotational invariance , in: Proceedings of the Twenty-First International Conference on Machine Learning, ICML ’04, Association for Computing Machinery, New York, NY, USA, 2004, p. 78 · 2004
Earlier work this paper cites.
M. Valtonen, H. Karttunen, The Three-Body Problem, Cambridge Univ. Press, Cambridge, UK, 2005
2005
Earlier work this paper cites.
doi:10.1017/S0022112010001217
P. J. SCHMID, Dynamic mode decomposition of numerical and experimental data, Journal of Fluid Mechanics 656 (2010) 5–28 · 2010
Earlier work this paper cites.
V. V. Makarov, Why is the moon synchronously rotating ?, Monthly Notices of the Royal Astronomical Society 434 (2013) L21–L25 · 2013
Earlier work this paper cites.
doi:https://doi.org/10.1016/j.ast.2014.12.030
K. Darvish, S. H. Pourtakdoust, N. Assadian, Linear and nonlinear control strategies for formation and station keeping of spacecrafts within the context of the three body problem , Aerospace Science and Technology 42 (2015) 12–24 · 2014
Earlier work this paper cites.
K. F. Wakker, Fundamentals of Astrodynamics, Institutional Repository Library, Delft, NL, 2015
2015
Earlier work this paper cites.
doi:10.1007/s00332-015-9258-5
M. O. Williams, I. G. Kevrekidis, C. W. Rowley, A data–driven approximation of the koopman operator: Extending dynamic mode decomposition , Journal of Nonlinear Science 25 (6) (2015) 1307–1346 · 2015
Cited alongside, same era.
Y. LeCun, Y. Bengio, G. Hinton, Deep learning, nature 521 (7553) (2015) 436–444
2015
Cited alongside, same era.
doi:10.1371/journal.pone.0150171
S. Brunton, B. Brunton, J. Proctor, J. Kutz, Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control, PloS one 11 (10 2015) · 2015
Cited alongside, same era.
doi:10.1007/978-3-319-22726-9
M. Valtonen, J. Anosova, K. Kholshevnikov, A. Mylläri, V. Orlov, K. Tanikawa, The Three-body Problem from Pythagoras to Hawking, Springer International Publishing, Cham, CH, 2016 · 2016
Cited alongside, same era.
S. Klus, C. Schütte, Towards tensor-based methods for the numerical approximation of the perron–frobenius and koopman operator, Journal of Computational Dynamics 3 (2) (2016) 139–161
2016
Cited alongside, same era.
doi:https://doi.org/10.1016/j.geomphys.2023.104883
A. Arsie, N. A. Balabanova, Collision trajectories and regularisation of two-body problem on s2 , Journal of Geometry and Physics 191 (2023) 104883 · 2023
Later among the works it cites.
P. M. Pires, C. F. de Melo, M. C. F. P. S. Zanardi, S. M. G. Winter, Celestial mechanics: new discoveries and challenges for space exploration. , The European Physical Journal Special Topics 232 (18-19) (2023) 2881 – 2887. URL https://link.springer.com/article/10.1140/epjs/s11734-023-01074-2
2023
Later among the works it cites.
P. Luke T., S. Daniel J., Local orbital elements for the circular restricted three-body problem. , Journal of Guidance, Control, and Dynamics 46 (12) (2023) 2275 – 2289. URL https://arc.aiaa.org/doi/10.2514/1.G007435
2023
Later among the works it cites.
doi:10.1109/SII55687.2023.10039188
S. Hagane, L. Jamone, G. Venture, Linearizing robotic manipulator’s dynamics using koopman operator and applying generalized predictive control, in: 2023 IEEE/SICE International Symposium on System Integration (SII), 2023, pp. 1–8 · 2023
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
P. Amaro-Seoane, et al., Laser interferometer space antenna (2017) · 2017
Cited alongside, same era.
doi:10.1038/s41467-018-07210-0
B. Lusch, J. N. Kutz, S. L. Brunton, Deep learning for universal linear embeddings of nonlinear dynamics , Nature Communications 9 (1) (Nov 2018) · 2018
Cited alongside, same era.
doi:10.1016/j.automatica.2018.03.046
M. Korda, I. Mezić, Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control , Automatica 93 (2018) 149–160 · 2018
Cited alongside, same era.
doi:10.2514/4.105210
H. Schaub, J. L. Junkins, Analytical Mechanics of Space Systems, 4th Edition, AIAA Education Series, Reston, VA, 2018 · 2018
Cited alongside, same era.
arXiv:https://doi.org/10.2514/1.A34390
G. Franzini, M. Innocenti, Relative motion dynamics in the restricted three-body problem , Journal of Spacecraft and Rockets 56 (5) (2019) 1322–1337 · 2019
Cited alongside, same era.
C. Folkestad, D. Pastor, I. Mezic, R. Mohr, M. Fonoberova, J. Burdick, Extended dynamic mode decomposition with learned koopman eigenfunctions for prediction and control, in: 2020 american control conference (acc), IEEE, 2020, pp. 3906–3913
2020
Cited alongside, same era.
doi:doi:10.2478/amns.2021.2.00300
S. Alhowaity, Computational algorithm to solve two–body problem using power series in geocentric system , Applied Mathematics and Nonlinear Sciences 8 (2) (2023) 39–46 · 2021
Cited alongside, same era.
A. Jin, F. Zhang, P. Huang, Data-driven optimal control of tethered space robot deployment with learning based koopman operator (2023) · 2023
Later among the works it cites.
Amaro-Seoane, et al., Astrophysics with the Laser Interferometer Space Antenna, Living Reviews in Relativity 26 (1) (2023) 2 · 2023
Later among the works it cites.
R. Power, K. Howell, Numerical methodology for extending koopman operator theory application in the crtbp, 2023
2023
Later among the works it cites.
doi:10.1109/LCSYS.2023.3329623
M. Tiwari, G. Nehma, B. Lusch, Computationally efficient data-driven discovery and linear representation of nonlinear systems for control, IEEE Control Systems Letters 7 (2023) 3373–3378 · 2023
Later among the works it cites.
M. Svec, S. Iles, J. Matusko, Predictive direct yaw moment control based on the koopman operator. , IEEE Transactions on Control Systems Technology, Control Systems Technology, IEEE Transactions on, IEEE Trans. Contr. Syst. Technol 31 (6) (2023) 2912 – 2919. URL https://portal.lib.fit.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=edseee&AN=edseee.10122214&site=eds-live
2023
Later among the works it cites.
doi:10.1016/j.neucom.2023.01.029
V. Zinage, E. Bakolas, Neural koopman lyapunov control , Neurocomputing 527 (2023) 174–183 · 2023
Later among the works it cites.
doi:10.3390/aerospace10020135
L. Ye, C. Liu, F. Liu, W. Zhang, H. Baoyin, The low fuel consumption keeping method of eccentricity under integrated keeping of inclination-longitude , Aerospace 10 (2) (2023) · 2023
Later among the works it cites.
D. Batic, M. Nowakowski, A. M. Abdelhaq, New vistas on the Laplace-Runge-Lenz vector, Reviews in Physics 10 (2023) 100084 · 2023
Later among the works it cites.
A. P. Wilmer, R. A. Bettinger, Lagrangian dynamics and the discovery of cislunar periodic orbits. , Nonlinear Dynamics: An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems 111 (1) (2023) 155 – 178. URL https://portal.lib.fit.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=edssjs&AN=edssjs.98923734&site=eds-live
2023
Later among the works it cites.
2023
Later among the works it cites.
doi:https://doi.org/10.1016/j.ast.2024.109048
C. Du, L. Song, J. Zhang, Y. Liu, A novel calculation method for low-thrust transfer trajectories in the earth-moon restricted three-body problem , Aerospace Science and Technology 147 (2024) 109048 · 2024
Closest in time.
C. R. Constante-Amores, A. J. Fox, C. E. P. D. Jesús, M. D. Graham, Data-driven koopman operator predictions of turbulent dynamics in models of shear flows (2024) · 2024
Closest in time.
doi:https://doi.org/10.1016/j.ast.2024.109515
R. Mao, T. Meng, K. Wang, J. Lei, W. Wang, Deep koopman-operator-based model predictive control for free-floating space robots with disturbance observer , Aerospace Science and Technology 154 (2024) 109515 · 2024
Closest in time.
Z. M. Manaa, A. M. Abdallah, M. A. Abido, S. S. A. Ali, Koopman-lqr controller for quadrotor uavs from data (2024) · 2024
Closest in time.
S. Servadio, W. Parker, R. Linares, Uncertainty propagation and filtering via the koopman operator in astrodynamics (2024) · 2024
Closest in time.
G. M. Nehma, M. Tiwari, M. Lingam, Advancements in spacecraft rendezvous: Leveraging koopman theory over clohessy-wiltshire equations, in: AIAA SCITECH 2025 Forum, American Institute of Aeronautics and Astronautics, Reston, Virginia, 2025
2025
Closest in time.
E. I. Abouelmagd, J. L. García Guirao, J. Llibre, On the periodic orbits of the perturbed two- and three-body problems , Galaxies 11 (2) (2023) 58, copyright - © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License; Last updated - 2023-11-24. URL https://www.mdpi.com/2075-4434/11/2/58
2075
Closest in time.
doi:10.1137/17m1125236
H. Arbabi, I. Mezić, Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the koopman operator , SIAM Journal on Applied Dynamical Systems 16 (4) (2017) 2096–2126 · 2096
Closest in time.