Old perturbative methods for a new problem in Celestial Mechanics: the space debris dynamics
Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N -body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems and they have the remarkable property to be constructive. A well-known application of pe...
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| Published in | Bollettino della Unione matematica italiana (2008) Vol. 16; no. 2; pp. 411 - 428 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.06.2023
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1972-6724 2198-2759 2198-2759 |
| DOI | 10.1007/s40574-023-00347-x |
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| Abstract | Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of
N
-body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems and they have the remarkable property to be constructive. A well-known application of perturbative techniques is represented by the construction of the so-called
proper elements
, which are quasi-invariants of the dynamics, obtained by removing the perturbing function to higher orders. They have been used to identify families of asteroids; more recently, they have been used in the context of space debris, which is the main core of this work. We describe the dynamics of space debris, considering a model including the Earth’s gravitational attraction, the influence of Sun and Moon, and the Solar radiation pressure. We construct a Lie series normalization procedure and we compute the proper elements associated to the orbital elements. To provide a concrete example, we analyze three different break-up events with nearby initial orbital elements. We use the information coming from proper elements to successfully group the fragments; the clusterization is supported by statistical data analysis and by machine learning methods. These results show that perturbative methods still play an important role in the study of the dynamics of space objects. |
|---|---|
| AbstractList | Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N-body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems and they have the remarkable property to be constructive. A well-known application of perturbative techniques is represented by the construction of the so-called proper elements, which are quasi-invariants of the dynamics, obtained by removing the perturbing function to higher orders. They have been used to identify families of asteroids; more recently, they have been used in the context of space debris, which is the main core of this work. We describe the dynamics of space debris, considering a model including the Earth’s gravitational attraction, the influence of Sun and Moon, and the Solar radiation pressure. We construct a Lie series normalization procedure and we compute the proper elements associated to the orbital elements. To provide a concrete example, we analyze three different break-up events with nearby initial orbital elements. We use the information coming from proper elements to successfully group the fragments; the clusterization is supported by statistical data analysis and by machine learning methods. These results show that perturbative methods still play an important role in the study of the dynamics of space objects. Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N -body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems and they have the remarkable property to be constructive. A well-known application of perturbative techniques is represented by the construction of the so-called proper elements , which are quasi-invariants of the dynamics, obtained by removing the perturbing function to higher orders. They have been used to identify families of asteroids; more recently, they have been used in the context of space debris, which is the main core of this work. We describe the dynamics of space debris, considering a model including the Earth’s gravitational attraction, the influence of Sun and Moon, and the Solar radiation pressure. We construct a Lie series normalization procedure and we compute the proper elements associated to the orbital elements. To provide a concrete example, we analyze three different break-up events with nearby initial orbital elements. We use the information coming from proper elements to successfully group the fragments; the clusterization is supported by statistical data analysis and by machine learning methods. These results show that perturbative methods still play an important role in the study of the dynamics of space objects. |
| Author | Celletti, Alessandra Vartolomei, Tudor |
| Author_xml | – sequence: 1 givenname: Alessandra orcidid: 0000-0001-8315-8433 surname: Celletti fullname: Celletti, Alessandra email: celletti@mat.uniroma2.it organization: Department of Mathematics, University of Roma Tor Vergata – sequence: 2 givenname: Tudor surname: Vartolomei fullname: Vartolomei, Tudor organization: Department of Mathematics, University of Roma Tor Vergata |
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| Cites_doi | 10.1086/104299 10.1126/science.168.3939.1569 10.1023/A:1011187405509 10.1086/106480 10.1007/BF00049444 10.1051/0004-6361:20030475 10.1007/s10569-022-10091-7 10.1007/s10569-019-9912-6 10.1093/mnras/staa713 10.1086/111116 10.1038/s41598-022-05696-9 10.1016/S0273-1177(01)00423-9 10.1007/s00332-014-9217-6 10.1093/mnras/stz1795 10.1006/icar.1994.1020 10.1007/s10569-015-9644-1 10.1007/s10569-016-9726-8 10.1017/9781009151122 10.1007/BF01230629 10.1007/s10569-022-10078-4 10.1137/17M1118671 10.1016/j.ijnonlinmec.2016.12.015 10.2307/j.ctv1v7zdn4.45 10.1016/j.icarus.2011.08.016 10.1093/mnras/stw927 10.1007/s10569-019-9895-3 10.1007/s10569-022-10064-w 10.1017/S1743921315008728 10.1007/s10569-022-10088-2 10.1006/icar.1993.1110 10.1007/BF00699724 10.1007/s10569-019-9906-4 10.1007/s10569-016-9746-4 10.1007/s10569-018-9865-1 10.1007/s10569-021-10021-z 10.1007/978-3-319-03762-2 10.1007/BF00693091 |
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| References | LemaitreAMorbidelliAProper elements for highly inclined asteroidal orbitsCelest. Mech. Dyn. Astron.19946029560825.70061 DepritACanonical transformations depending on a small parameterCelest. Mech.1969112302536110172.26002 CellettiAGachetFGaleşCPucaccoGEfthymiopoulosCDynamical models and the onset of chaos in space debrisInt. J. Nonlinear Mech.20179047163 KneževićZMilaniASynthetic proper elements for outer main belt asteroidsCelest. Mech. Dyn. Astron.20007817460992.85502 Kozai, Y.: The dynamical evolution of the Hirayama family. In: Gehrels, T. (ed.) Asteroids. Univ. Arizona Press, pp. 334–335 (1979) LemaitreAProper elements: what are they?Celest. Mech. Dyn. Astron.199256103119 CellettiAGalesCRodriguez-FernandezVVasileMClassification of regular and chaotic motions in Hamiltonian systems with deep learningSci. Rep.2022121890 KneževićZMilaniAProper element catalogs and asteroid familiesAstron. Astrophys.200340311651173 Apetrii, M., Celletti, A., Efthymiopoulos, E., Galeş, C., Vartolomei, T.: On a simulator of break-up events for space debris. Work Progress (2022) CellettiAGaleşCLhotkaCResonance in the Earth’s space environmentNonlinear Sci. Num. Sim.20208440562501444.70008 Fenucci, M., Gronchi, G., Saillenfest, M.: Proper elements for resonant planet-crossing asteroids. Celest. Mech. Dynam. Astron. 3 (2022) SchubartJAdditional results on orbits of Hilda-type asteroidsAstron. Astrophys.1991241297302 CellettiAGaleşCDynamics of resonances and equilibria of Low Earth ObjectsSIAM J. Appl. Dyn. Syst.20181720323537556541390.70029 HirayamaKGroups of asteroids probably of common originAstron. J.191831185188 BreenPGFoleyCNBoekholtTPortegies ZwartSNewton versus the machine: solving the chaotic three-body problem using deep neural networksMNRAS2020494224652470 Rosengren, A., Bombardelli, C., Amato, D.: Geocentric proper orbital elements. In: AAS/Division of dynamical astronomy meeting, vol. 51, p. P3 (2019) YuasaMTheory of secular perturbations of asteroids including terms of higher orders and higher degreesPubl. Astron. Soc. Jpn.197325399 Knežević, Z.: Asteroid family identification: history and state of the art. In: Chesley, S.R., Morbidelli, A., Jedicke, R., Farnocchia, D. (eds.) Proceedings IAU Symposium No. 318, 2015, International Astronomical Union (2016) BrouwerDSecular variations of the orbital elements of minor planetsAstron. J.195156932 CasanovaDPetitALemaitreALong-term evolution of space debris under the J2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_2$$\end{document} effect, the solar radiation pressure and the solar and lunar perturbationsCelest. Mech. Dyn. Astr.20151232232381428.70025 Tisserand, F.: Traité de Mécanique Céleste, I, Ch. 23. Édition Jacques Gabay, Paris (1889) JohnsonNLKriskoPHLieuJ-CAm-MeadorPDNASA’s new break-up model of EVOLVE 4.0Adv. Sp. Res.200128913771384 Knežević, Z., Lemaitre, A., Milani, A.: The determination of asteroid proper elements. In: Bottke, W., et al. (ed.) Asteroids III. Arizona Univ. Press and LPI, Tucson, p. 603 (2003) DepritAHenrardJRomAAnalytical lunar ephemeris: Delaunay’s theoryAstron. J.19717632692720216.50304 SchubartJThree characteristic parameters of orbits of Hilda-type asteroidsAstron. Astrophys.19821141200204 Schettino, G., Alessi, E.M., Rossi, A., Valsecchi, G.B.: A frequency portrait of Low Earth Orbits. Celest. Mech. Dyn. Astron. 131(35) (2019) DepritAHenrardJRomALunar ephemeris: Delaunay’s theory revisitedScience1970168393915691570 GiorgilliANotes on Hamiltonian Dynamical Systems2022CambridgeCambridge University Press07504269 CarrubaVAljbaaeSDomingosRCHuamanMBarlettaWMachine learning applied to asteroid dynamicsCelest. Mech. Dyn. Astron.202213436446272707592111 CarrubaVAljbaaeSDomingosRCIdentification of asteroid groups in the z1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_1$$\end{document} and z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_2$$\end{document} nonlinear secular resonances through genetic algorithmsCelest. Mech. Dyn. Astron.2021133241472.70033 CarpinoMMilaniANobiliAMLong-term numerical integrations and synthetic theories for the motion of the outer planetsAstron. Astrophys.198718111821940618.70006 NovakovicBVokrouhlickyDSpotoFNesvornyDAsteroid families: properties, recent advances, and future opportunitiesCelest. Mech. Dyn. Astron.2022134344456206 Delaunay, C.E.: Theorie du Mouvement de la Lune, Vol. I and Vol. II. Mallet-Bachelier, Paris (1867) Rosengren, A., Amato, D., Bombardelli, C., Jah, M.: Resident space object proper orbital elements. In: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Kaanapali, Maui, HI, Paper AAS 19-557 (2019) CellettiAGaleşCOn the dynamics of space debris: 1:1 and 2:1 resonancesJ. Nonlinear Sci.20142461231126232752241302.70036 EfthymiopoulosCCanonical perturbation theory, stability and diffusion in Hamiltonian systems: applications in dynamical astronomyWorkshop Ser. Assoc. Argent. Astron.201133146 KneževićZMilaniAAre the analytical proper elements of asteroids still needed?Celest. Mech. Dyn. Astron.20191312739595641451.70045 CellettiAPucaccoGVartolomeiTReconnecting groups of space debris to their parent body through proper elementsNat. Sci. Rep.20211122676 Bien, R., Schubart, J.: Methods of determination of periods in the motion of asteroids. In: Asteroids, Comets, and Meteors (1983) AAVV, NASA Standard break-up Model 1998 Revision, prepared by Lockheed Martin Space Mission Systems & Services for NASA (1998) KneževićZMilaniADvorakRHenrardJSynthetic proper elements for outer main belt asteroidsNew Developments in the Dynamics of Planetary Systems2001NetherlandsSpringer1274.85012 NovacovićBCellinoAKneževićZFamilies among high-inclination asteroidsIcarus20112166981 HirayamaKFamilies of asteroidsJpn. J. Astron. Geophys.1922155 GachetFCellettiAPucaccoGEfthymiopoulosCGeostationary secular dynamics revisited: application to high area-to-mass ratio objectsCelest. Mech. Dyn. Astr.20171282-314918136583481367.70054 BernardEIntroduction to Machine Learning2021ChampaignWolfram Media Inc CarrubaVAljbaaeSLucchiniAMachine-learning identification of asteroid groupsMNRAS2019488113771386 CellettiAGaleşCPucaccoGRosengrenAAnalytical development of the lunisolar disturbing function and the critical inclination secular resonanceCelest. Mech. Dyn. Astron.2017127325928336075151374.70029 MilaniAKneževićZSecular perturbation theory and computation of asteroid proper elementsMech. Dyn. Astron.19904934741111034130724.70008 Wolfram Documentation Center for “KMeans”, https://reference.wolfram.com/language/ref/method/KMeans.html Williams, J.G.: Secular Perturbations in the Solar System. Ph.D. thesis, University of California, Los Angeles (1969) BrandtSData Analysis2014ChamSpringer Gkolias, I., Colombo, C.: Towards a sustainable exploitation of the geosynchronous orbital region. Celest. Mech. Dyn. Astr. 131(19) (2019) MorbidelliAAsteroid secular resonant proper elementsIcarus19931054866 SkoulidouDKRosengrenAJTsiganisKVoyatzisGDynamical lifetime survey of geostationary transfer orbitsCelest. Mech. Dyn. Astron.201813077 CellettiAPucaccoGVartolomeiTProper elements for space debrisCelest. Mech. Dyn. Astr.20221341143993021490.70040 Wu, D., Rosengren, A.J.: RSO proper elements for space situational and domain awareness. In: Advanced Maui Optical and Space Surveillance Technologies Conference AMOS (2021) MilaniAKneževićZAsteroid proper elements and the dynamical structure of the asteroid main beltIcarus1994107219254 LhotkaCCellettiAGaleşCPoynting–Robertson drag and solar wind in the space debris problemMon. Not. R. Ast. Soc.2016460802815 A Celletti (347_CR16) 2017; 127 DK Skoulidou (347_CR53) 2018; 130 347_CR48 347_CR49 Z Knežević (347_CR35) 2001 A Celletti (347_CR19) 2022; 134 NL Johnson (347_CR32) 2001; 28 347_CR4 K Hirayama (347_CR31) 1922; 1 347_CR1 M Yuasa (347_CR58) 1973; 25 347_CR2 J Schubart (347_CR51) 1982; 114 V Carruba (347_CR10) 2021; 133 A Giorgilli (347_CR28) 2022 A Milani (347_CR44) 1994; 107 A Celletti (347_CR17) 2020; 84 A Morbidelli (347_CR45) 1993; 105 M Carpino (347_CR8) 1987; 181 A Celletti (347_CR14) 2018; 17 C Lhotka (347_CR42) 2016; 460 J Schubart (347_CR52) 1991; 241 347_CR54 347_CR50 347_CR55 347_CR56 347_CR57 D Casanova (347_CR12) 2015; 123 E Bernard (347_CR3) 2021 F Gachet (347_CR27) 2017; 128 Z Knežević (347_CR36) 2003; 403 A Deprit (347_CR23) 1970; 168 B Novakovic (347_CR47) 2022; 134 A Celletti (347_CR18) 2021; 11 A Deprit (347_CR24) 1971; 76 K Hirayama (347_CR30) 1918; 31 D Brouwer (347_CR7) 1951; 56 A Celletti (347_CR15) 2017; 90 347_CR21 A Deprit (347_CR22) 1969; 1 347_CR26 B Novacović (347_CR46) 2011; 216 A Lemaitre (347_CR40) 1992; 56 347_CR29 A Celletti (347_CR20) 2022; 12 S Brandt (347_CR5) 2014 Z Knežević (347_CR34) 2000; 78 C Efthymiopoulos (347_CR25) 2011; 3 A Celletti (347_CR13) 2014; 24 347_CR38 347_CR39 347_CR33 A Lemaitre (347_CR41) 1994; 60 V Carruba (347_CR9) 2019; 488 Z Knežević (347_CR37) 2019; 131 V Carruba (347_CR11) 2022; 134 A Milani (347_CR43) 1990; 49 PG Breen (347_CR6) 2020; 494 |
| References_xml | – reference: GiorgilliANotes on Hamiltonian Dynamical Systems2022CambridgeCambridge University Press07504269 – reference: LemaitreAMorbidelliAProper elements for highly inclined asteroidal orbitsCelest. Mech. Dyn. Astron.19946029560825.70061 – reference: CellettiAGaleşCDynamics of resonances and equilibria of Low Earth ObjectsSIAM J. Appl. Dyn. Syst.20181720323537556541390.70029 – reference: Tisserand, F.: Traité de Mécanique Céleste, I, Ch. 23. Édition Jacques Gabay, Paris (1889) – reference: BrouwerDSecular variations of the orbital elements of minor planetsAstron. J.195156932 – reference: Knežević, Z., Lemaitre, A., Milani, A.: The determination of asteroid proper elements. In: Bottke, W., et al. (ed.) Asteroids III. Arizona Univ. Press and LPI, Tucson, p. 603 (2003) – reference: SchubartJAdditional results on orbits of Hilda-type asteroidsAstron. Astrophys.1991241297302 – reference: CellettiAGaleşCPucaccoGRosengrenAAnalytical development of the lunisolar disturbing function and the critical inclination secular resonanceCelest. Mech. Dyn. Astron.2017127325928336075151374.70029 – reference: Apetrii, M., Celletti, A., Efthymiopoulos, E., Galeş, C., Vartolomei, T.: On a simulator of break-up events for space debris. Work Progress (2022) – reference: HirayamaKGroups of asteroids probably of common originAstron. J.191831185188 – reference: Schettino, G., Alessi, E.M., Rossi, A., Valsecchi, G.B.: A frequency portrait of Low Earth Orbits. Celest. Mech. Dyn. Astron. 131(35) (2019) – reference: CellettiAPucaccoGVartolomeiTProper elements for space debrisCelest. Mech. Dyn. Astr.20221341143993021490.70040 – reference: CellettiAGaleşCLhotkaCResonance in the Earth’s space environmentNonlinear Sci. Num. Sim.20208440562501444.70008 – reference: AAVV, NASA Standard break-up Model 1998 Revision, prepared by Lockheed Martin Space Mission Systems & Services for NASA (1998) – reference: BernardEIntroduction to Machine Learning2021ChampaignWolfram Media Inc – reference: CasanovaDPetitALemaitreALong-term evolution of space debris under the J2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_2$$\end{document} effect, the solar radiation pressure and the solar and lunar perturbationsCelest. Mech. Dyn. Astr.20151232232381428.70025 – reference: Wolfram Documentation Center for “KMeans”, https://reference.wolfram.com/language/ref/method/KMeans.html – reference: DepritAHenrardJRomAAnalytical lunar ephemeris: Delaunay’s theoryAstron. J.19717632692720216.50304 – reference: Wu, D., Rosengren, A.J.: RSO proper elements for space situational and domain awareness. In: Advanced Maui Optical and Space Surveillance Technologies Conference AMOS (2021) – reference: NovakovicBVokrouhlickyDSpotoFNesvornyDAsteroid families: properties, recent advances, and future opportunitiesCelest. Mech. Dyn. Astron.2022134344456206 – reference: YuasaMTheory of secular perturbations of asteroids including terms of higher orders and higher degreesPubl. Astron. Soc. Jpn.197325399 – reference: CarpinoMMilaniANobiliAMLong-term numerical integrations and synthetic theories for the motion of the outer planetsAstron. Astrophys.198718111821940618.70006 – reference: CellettiAPucaccoGVartolomeiTReconnecting groups of space debris to their parent body through proper elementsNat. Sci. Rep.20211122676 – reference: NovacovićBCellinoAKneževićZFamilies among high-inclination asteroidsIcarus20112166981 – reference: Gkolias, I., Colombo, C.: Towards a sustainable exploitation of the geosynchronous orbital region. Celest. Mech. Dyn. Astr. 131(19) (2019) – reference: LhotkaCCellettiAGaleşCPoynting–Robertson drag and solar wind in the space debris problemMon. Not. R. Ast. Soc.2016460802815 – reference: MilaniAKneževićZAsteroid proper elements and the dynamical structure of the asteroid main beltIcarus1994107219254 – reference: Bien, R., Schubart, J.: Methods of determination of periods in the motion of asteroids. In: Asteroids, Comets, and Meteors (1983) – reference: Rosengren, A., Bombardelli, C., Amato, D.: Geocentric proper orbital elements. In: AAS/Division of dynamical astronomy meeting, vol. 51, p. P3 (2019) – reference: Fenucci, M., Gronchi, G., Saillenfest, M.: Proper elements for resonant planet-crossing asteroids. Celest. Mech. Dynam. Astron. 3 (2022) – reference: Kozai, Y.: The dynamical evolution of the Hirayama family. In: Gehrels, T. (ed.) Asteroids. Univ. Arizona Press, pp. 334–335 (1979) – reference: JohnsonNLKriskoPHLieuJ-CAm-MeadorPDNASA’s new break-up model of EVOLVE 4.0Adv. Sp. Res.200128913771384 – reference: CarrubaVAljbaaeSDomingosRCHuamanMBarlettaWMachine learning applied to asteroid dynamicsCelest. Mech. Dyn. Astron.202213436446272707592111 – reference: GachetFCellettiAPucaccoGEfthymiopoulosCGeostationary secular dynamics revisited: application to high area-to-mass ratio objectsCelest. Mech. Dyn. Astr.20171282-314918136583481367.70054 – reference: Rosengren, A., Amato, D., Bombardelli, C., Jah, M.: Resident space object proper orbital elements. In: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Kaanapali, Maui, HI, Paper AAS 19-557 (2019) – reference: HirayamaKFamilies of asteroidsJpn. J. Astron. Geophys.1922155 – reference: SchubartJThree characteristic parameters of orbits of Hilda-type asteroidsAstron. Astrophys.19821141200204 – reference: CellettiAGachetFGaleşCPucaccoGEfthymiopoulosCDynamical models and the onset of chaos in space debrisInt. J. Nonlinear Mech.20179047163 – reference: DepritAHenrardJRomALunar ephemeris: Delaunay’s theory revisitedScience1970168393915691570 – reference: LemaitreAProper elements: what are they?Celest. Mech. Dyn. Astron.199256103119 – reference: KneževićZMilaniASynthetic proper elements for outer main belt asteroidsCelest. Mech. Dyn. Astron.20007817460992.85502 – reference: Delaunay, C.E.: Theorie du Mouvement de la Lune, Vol. I and Vol. II. Mallet-Bachelier, Paris (1867) – reference: MilaniAKneževićZSecular perturbation theory and computation of asteroid proper elementsMech. Dyn. Astron.19904934741111034130724.70008 – reference: Williams, J.G.: Secular Perturbations in the Solar System. Ph.D. thesis, University of California, Los Angeles (1969) – reference: BreenPGFoleyCNBoekholtTPortegies ZwartSNewton versus the machine: solving the chaotic three-body problem using deep neural networksMNRAS2020494224652470 – reference: EfthymiopoulosCCanonical perturbation theory, stability and diffusion in Hamiltonian systems: applications in dynamical astronomyWorkshop Ser. Assoc. Argent. Astron.201133146 – reference: KneževićZMilaniAAre the analytical proper elements of asteroids still needed?Celest. Mech. Dyn. Astron.20191312739595641451.70045 – reference: CellettiAGalesCRodriguez-FernandezVVasileMClassification of regular and chaotic motions in Hamiltonian systems with deep learningSci. Rep.2022121890 – reference: CarrubaVAljbaaeSLucchiniAMachine-learning identification of asteroid groupsMNRAS2019488113771386 – reference: CarrubaVAljbaaeSDomingosRCIdentification of asteroid groups in the z1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_1$$\end{document} and z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_2$$\end{document} nonlinear secular resonances through genetic algorithmsCelest. Mech. Dyn. Astron.2021133241472.70033 – reference: KneževićZMilaniADvorakRHenrardJSynthetic proper elements for outer main belt asteroidsNew Developments in the Dynamics of Planetary Systems2001NetherlandsSpringer1274.85012 – reference: KneževićZMilaniAProper element catalogs and asteroid familiesAstron. Astrophys.200340311651173 – reference: MorbidelliAAsteroid secular resonant proper elementsIcarus19931054866 – reference: CellettiAGaleşCOn the dynamics of space debris: 1:1 and 2:1 resonancesJ. Nonlinear Sci.20142461231126232752241302.70036 – reference: BrandtSData Analysis2014ChamSpringer – reference: Knežević, Z.: Asteroid family identification: history and state of the art. In: Chesley, S.R., Morbidelli, A., Jedicke, R., Farnocchia, D. (eds.) Proceedings IAU Symposium No. 318, 2015, International Astronomical Union (2016) – reference: SkoulidouDKRosengrenAJTsiganisKVoyatzisGDynamical lifetime survey of geostationary transfer orbitsCelest. Mech. Dyn. Astron.201813077 – reference: DepritACanonical transformations depending on a small parameterCelest. Mech.1969112302536110172.26002 – volume: 31 start-page: 185 year: 1918 ident: 347_CR30 publication-title: Astron. J. doi: 10.1086/104299 – volume: 168 start-page: 1569 issue: 3939 year: 1970 ident: 347_CR23 publication-title: Science doi: 10.1126/science.168.3939.1569 – volume: 1 start-page: 55 year: 1922 ident: 347_CR31 publication-title: Jpn. J. Astron. Geophys. – volume: 78 start-page: 17 year: 2000 ident: 347_CR34 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1023/A:1011187405509 – volume: 241 start-page: 297 year: 1991 ident: 347_CR52 publication-title: Astron. Astrophys. – volume: 56 start-page: 9 year: 1951 ident: 347_CR7 publication-title: Astron. J. doi: 10.1086/106480 – volume: 49 start-page: 347 year: 1990 ident: 347_CR43 publication-title: Mech. Dyn. Astron. doi: 10.1007/BF00049444 – volume: 403 start-page: 1165 year: 2003 ident: 347_CR36 publication-title: Astron. Astrophys. doi: 10.1051/0004-6361:20030475 – ident: 347_CR55 – volume-title: New Developments in the Dynamics of Planetary Systems year: 2001 ident: 347_CR35 – volume: 134 start-page: 34 year: 2022 ident: 347_CR47 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-022-10091-7 – ident: 347_CR50 doi: 10.1007/s10569-019-9912-6 – volume: 494 start-page: 2465 issue: 2 year: 2020 ident: 347_CR6 publication-title: MNRAS doi: 10.1093/mnras/staa713 – volume: 76 start-page: 269 issue: 3 year: 1971 ident: 347_CR24 publication-title: Astron. J. doi: 10.1086/111116 – volume: 12 start-page: 1890 year: 2022 ident: 347_CR20 publication-title: Sci. Rep. doi: 10.1038/s41598-022-05696-9 – volume: 28 start-page: 1377 issue: 9 year: 2001 ident: 347_CR32 publication-title: Adv. Sp. Res. doi: 10.1016/S0273-1177(01)00423-9 – ident: 347_CR49 – volume: 24 start-page: 1231 issue: 6 year: 2014 ident: 347_CR13 publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-014-9217-6 – volume: 488 start-page: 1377 issue: 1 year: 2019 ident: 347_CR9 publication-title: MNRAS doi: 10.1093/mnras/stz1795 – volume: 107 start-page: 219 year: 1994 ident: 347_CR44 publication-title: Icarus doi: 10.1006/icar.1994.1020 – volume: 114 start-page: 200 issue: 1 year: 1982 ident: 347_CR51 publication-title: Astron. Astrophys. – volume: 123 start-page: 223 year: 2015 ident: 347_CR12 publication-title: Celest. Mech. Dyn. Astr. doi: 10.1007/s10569-015-9644-1 – volume: 127 start-page: 259 issue: 3 year: 2017 ident: 347_CR16 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-016-9726-8 – volume-title: Notes on Hamiltonian Dynamical Systems year: 2022 ident: 347_CR28 doi: 10.1017/9781009151122 – ident: 347_CR56 – ident: 347_CR4 – volume: 11 start-page: 22676 year: 2021 ident: 347_CR18 publication-title: Nat. Sci. Rep. – ident: 347_CR21 – volume: 1 start-page: 12 year: 1969 ident: 347_CR22 publication-title: Celest. Mech. doi: 10.1007/BF01230629 – ident: 347_CR26 doi: 10.1007/s10569-022-10078-4 – volume: 17 start-page: 203 year: 2018 ident: 347_CR14 publication-title: SIAM J. Appl. Dyn. Syst. doi: 10.1137/17M1118671 – ident: 347_CR57 – ident: 347_CR1 – volume: 90 start-page: 47 year: 2017 ident: 347_CR15 publication-title: Int. J. Nonlinear Mech. doi: 10.1016/j.ijnonlinmec.2016.12.015 – ident: 347_CR39 doi: 10.2307/j.ctv1v7zdn4.45 – volume: 216 start-page: 69 year: 2011 ident: 347_CR46 publication-title: Icarus doi: 10.1016/j.icarus.2011.08.016 – volume-title: Introduction to Machine Learning year: 2021 ident: 347_CR3 – volume: 460 start-page: 802 year: 2016 ident: 347_CR42 publication-title: Mon. Not. R. Ast. Soc. doi: 10.1093/mnras/stw927 – ident: 347_CR29 doi: 10.1007/s10569-019-9895-3 – volume: 3 start-page: 3 year: 2011 ident: 347_CR25 publication-title: Workshop Ser. Assoc. Argent. Astron. – volume: 134 start-page: 11 year: 2022 ident: 347_CR19 publication-title: Celest. Mech. Dyn. Astr. doi: 10.1007/s10569-022-10064-w – ident: 347_CR33 doi: 10.1017/S1743921315008728 – volume: 134 start-page: 36 year: 2022 ident: 347_CR11 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-022-10088-2 – volume: 105 start-page: 48 year: 1993 ident: 347_CR45 publication-title: Icarus doi: 10.1006/icar.1993.1110 – ident: 347_CR54 – volume: 181 start-page: 182 issue: 1 year: 1987 ident: 347_CR8 publication-title: Astron. Astrophys. – volume: 56 start-page: 103 year: 1992 ident: 347_CR40 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00699724 – volume: 131 start-page: 27 year: 2019 ident: 347_CR37 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-019-9906-4 – ident: 347_CR38 – volume: 128 start-page: 149 issue: 2-3 year: 2017 ident: 347_CR27 publication-title: Celest. Mech. Dyn. Astr. doi: 10.1007/s10569-016-9746-4 – volume: 130 start-page: 77 year: 2018 ident: 347_CR53 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-018-9865-1 – ident: 347_CR2 – volume: 133 start-page: 24 year: 2021 ident: 347_CR10 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-021-10021-z – volume-title: Data Analysis year: 2014 ident: 347_CR5 doi: 10.1007/978-3-319-03762-2 – volume: 25 start-page: 399 year: 1973 ident: 347_CR58 publication-title: Publ. Astron. Soc. Jpn. – volume: 84 year: 2020 ident: 347_CR17 publication-title: Nonlinear Sci. Num. Sim. – volume: 60 start-page: 29 year: 1994 ident: 347_CR41 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00693091 – ident: 347_CR48 |
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N
-body problems in Celestial Mechanics. Such... Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N-body problems in Celestial Mechanics. Such... |
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| SubjectTerms | Celestial mechanics Data analysis Dynamics Hamiltonian functions Machine learning Mathematics Mathematics and Statistics Orbital elements Radiation pressure Solar radiation Space debris |
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| Title | Old perturbative methods for a new problem in Celestial Mechanics: the space debris dynamics |
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