From perturbative methods to machine learning techniques in space science
Perturbation theory is a very useful tool to investigate the dynamics of models in space science. We start by presenting some results obtained implementing classical perturbation theory to investigate the motion of space debris, which are objects that populate the sky around the Earth after a satell...
Saved in:
| Published in | Bollettino della Unione matematica italiana (2008) Vol. 18; no. 1; pp. 149 - 166 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.03.2025
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1972-6724 2198-2759 |
| DOI | 10.1007/s40574-024-00422-x |
Cover
| Abstract | Perturbation theory is a very useful tool to investigate the dynamics of models in space science. We start by presenting some results obtained implementing classical perturbation theory to investigate the motion of space debris, which are objects that populate the sky around the Earth after a satellite break-up event. When dealing with two or more break-up events, a clusterization of the fragments can be computed using machine learning techniques. We also present the celebrated KAM theory for symplectic and conformally symplectic systems. We recall several computer-assisted results in Celestial Mechanics in conservative and dissipative settings. Finally, we consider the spin-orbit problem and we show how machine learning methods can be conveniently used to classify regular and chaotic motions. |
|---|---|
| AbstractList | Perturbation theory is a very useful tool to investigate the dynamics of models in space science. We start by presenting some results obtained implementing classical perturbation theory to investigate the motion of space debris, which are objects that populate the sky around the Earth after a satellite break-up event. When dealing with two or more break-up events, a clusterization of the fragments can be computed using machine learning techniques. We also present the celebrated KAM theory for symplectic and conformally symplectic systems. We recall several computer-assisted results in Celestial Mechanics in conservative and dissipative settings. Finally, we consider the spin-orbit problem and we show how machine learning methods can be conveniently used to classify regular and chaotic motions. |
| Author | Celletti, Alessandra |
| Author_xml | – sequence: 1 givenname: Alessandra orcidid: 0000-0001-8315-8433 surname: Celletti fullname: Celletti, Alessandra |
| BookMark | eNotkMFOwzAMhiMEEmPsBThF4hxwnKZpjmhiMGkSl92jLPVYpzUtSYfG29MxDpYvn_7f_u7YdewiMfYg4UkCmOdcgDaFABwHCkRxumITlLYSaLS9ZhNpDYrSYHHLZjnvAUBKVRlrJmy5SF3Le0rDMW380HwTb2nYdXXmQ8dbH3ZNJH4gn2ITP_lAYRebryNl3kSeex-I59BQDHTPbrb-kGn2v6dsvXhdz9_F6uNtOX9ZiYAGBqHrwqsSTKgr9ApqDZUlVYcgg93WmwC6krXy0lpJm9JKj2g1lEAYEEurpuzxEtun7nzH4PbdMcWx0Slpzg9rLEcKL1RIXc6Jtq5PTevTj5PgztLcRZobpbk_ae6kfgEQ1mEU |
| Cites_doi | 10.1090/pspum/069/1858536 10.1070/RM1977v032n06ABEH003859 10.1086/106480 10.1070/RM1963v018n05ABEH004130 10.1007/BF00048985 10.1007/s10569-022-10064-w 10.1016/S0273-1177(01)00423-9 10.1088/0951-7715/11/3/015 10.1016/j.cnsns.2021.106111 10.1090/S0273-0979-1990-15848-3 10.1016/j.jde.2013.05.001 10.1007/s10569-005-6215-x 10.1007/BF00945107 10.1007/BF00728351 10.1088/0951-7715/18/4/017 10.1086/104299 10.1007/s10569-024-10205-3 10.1007/BF00049444 10.1016/j.cnsns.2023.107556 10.1023/A:1011187405509 10.1023/A:1011139523256 10.1007/BF01399536 10.1007/s10208-016-9339-3 10.1007/s10569-023-10157-0 10.1007/978-3-540-85146-2 10.1007/978-3-642-61215-2_2 10.1088/0951-7715/18/2/020 10.1007/BF00945951 10.1016/j.icarus.2005.03.017 10.1137/S0036144595284180 |
| ContentType | Journal Article |
| Copyright | Copyright Springer Nature B.V. 2025 |
| Copyright_xml | – notice: Copyright Springer Nature B.V. 2025 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s40574-024-00422-x |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2198-2759 |
| EndPage | 166 |
| ExternalDocumentID | 10_1007_s40574_024_00422_x |
| GroupedDBID | -~X 0R~ 203 2KM 4.4 406 8UJ 96X AAAVM AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAYIU AAYQN AAYTO AAYXX AAZMS ABAKF ABBRH ABDBE ABDZT ABECU ABFSG ABFTV ABHLI ABJOX ABKCH ABMQK ABPLI ABQBU ABTEG ABTKH ABTMW ABXPI ACAOD ACDTI ACGFS ACHSB ACIWK ACKNC ACMLO ACNCT ACOKC ACPIV ACSTC ACZOJ ADHHG ADHIR ADKNI ADKPE ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGNC AEJHL AEJRE AEMSY AEOHA AEPYU AESKC AETCA AEVLU AEXYK AEZWR AFBBN AFDZB AFFNX AFHIU AFLOW AFOHR AFQWF AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AIAKS AIGIU AILAN AITGF AIXLP AJBLW AJRNO AJZVZ AKLTO ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMXSW AMYLF AMYQR ANMIH ARMRJ ASPBG ATHPR AUKKA AVWKF AXYYD AYFIA AYJHY BAPOH BGNMA CITATION CSCUP DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FERAY FIGPU FINBP FNLPD FRRFC FSGXE FYJPI GGCAI GGRSB GJIRD HRMNR I0C IKXTQ ITM IWAJR J-C JBSCW JZLTJ KOV LLZTM M4Y NPVJJ NQJWS NU0 O9J PT4 RLLFE ROL RSV SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW SSXJD STPWE TSG UG4 UOJIU UPT UTJUX UZXMN VFIZW W48 ZMTXR ZY4 ABRTQ |
| ID | FETCH-LOGICAL-c270t-5d4a3607cd82a30d5089e3dcc1c9fdbc0581d3a1991eb691a2295060e2c22693 |
| ISSN | 1972-6724 |
| IngestDate | Sun Jul 13 03:48:56 EDT 2025 Tue Jul 01 05:18:00 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c270t-5d4a3607cd82a30d5089e3dcc1c9fdbc0581d3a1991eb691a2295060e2c22693 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-8315-8433 |
| OpenAccessLink | https://doi.org/10.1007/s40574-024-00422-x |
| PQID | 3172759526 |
| PQPubID | 2044283 |
| PageCount | 18 |
| ParticipantIDs | proquest_journals_3172759526 crossref_primary_10_1007_s40574_024_00422_x |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2025-03-01 |
| PublicationDateYYYYMMDD | 2025-03-01 |
| PublicationDate_xml | – month: 03 year: 2025 text: 2025-03-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg |
| PublicationTitle | Bollettino della Unione matematica italiana (2008) |
| PublicationYear | 2025 |
| Publisher | Springer Nature B.V |
| Publisher_xml | – name: Springer Nature B.V |
| References | R de la Llave (422_CR22) 2005; 18 J Moser (422_CR37) 1967; 169 A Milani (422_CR35) 1990; 49 A Celletti (422_CR8) 1990; 41 A Celletti (422_CR16) 1890; 12 D Wu (422_CR40) 2023; 135 D Brouwer (422_CR4) 1951; 56 A Celletti (422_CR17) 1990; 50 A Celletti (422_CR18) 2021; 11 A Celletti (422_CR12) 2006; 95 RC Calleja (422_CR5) 2013; 255 422_CR1 K Hirayama (422_CR27) 1918; 31 J Moser (422_CR36) 1962; 1962 N Johnson (422_CR28) 2001; 28 422_CR10 A Celletti (422_CR19) 2022; 134 422_CR32 H Koch (422_CR30) 1996; 38 422_CR11 A Celletti (422_CR20) 2023; 16 M Hénon (422_CR26) 1966; 3 422_CR33 SJ Peale (422_CR39) 2005; 178 RC Calleja (422_CR6) 2022; 106 422_CR38 A Celletti (422_CR13) 2007; 187 U Locatelli (422_CR34) 2000; 78 A Celletti (422_CR9) 1990; 41 F Gabern (422_CR25) 2005; 18 VI Arnol’d (422_CR2) 1963; 18 RC Calleja (422_CR7) 2022; 32 HW Broer (422_CR3) 1998; 11 Z Knežević (422_CR29) 2000; 78 422_CR21 R de la Llave (422_CR23) 1990; 22 A Celletti (422_CR14) 2023; 127 A Celletti (422_CR15) 1996; 64 422_CR24 AN Kolmogorov (422_CR31) 1954; 98 |
| References_xml | – ident: 422_CR21 doi: 10.1090/pspum/069/1858536 – ident: 422_CR38 doi: 10.1070/RM1977v032n06ABEH003859 – volume: 11 start-page: 22676 year: 2021 ident: 422_CR18 publication-title: Nat. Sci. Rep. – volume: 56 start-page: 9 year: 1951 ident: 422_CR4 publication-title: Astron. J. doi: 10.1086/106480 – volume: 16 start-page: 411 year: 2023 ident: 422_CR20 publication-title: BUMI – volume: 18 start-page: 9 issue: 5 year: 1963 ident: 422_CR2 publication-title: Russ. Math. Surv. doi: 10.1070/RM1963v018n05ABEH004130 – ident: 422_CR32 – volume: 187 start-page: 134 issue: 878 year: 2007 ident: 422_CR13 publication-title: Mem. Am. Math. Soc. – volume: 50 start-page: 31 issue: 1 year: 1990 ident: 422_CR17 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00048985 – volume: 12 start-page: 2022 year: 1890 ident: 422_CR16 publication-title: Nat. Sci. Rep. – volume: 134 start-page: 11 issue: 2 year: 2022 ident: 422_CR19 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-022-10064-w – volume: 28 start-page: 1377 issue: 9 year: 2001 ident: 422_CR28 publication-title: Adv. Space Res. doi: 10.1016/S0273-1177(01)00423-9 – volume: 32 start-page: 1 issue: 4 year: 2022 ident: 422_CR7 publication-title: J. Nonlinear Sci. – volume: 11 start-page: 667 year: 1998 ident: 422_CR3 publication-title: Nonlinearity doi: 10.1088/0951-7715/11/3/015 – volume: 106 year: 2022 ident: 422_CR6 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2021.106111 – volume: 22 start-page: 85 issue: 1 year: 1990 ident: 422_CR23 publication-title: Bull. Am. Math. Soc. (N.S.) doi: 10.1090/S0273-0979-1990-15848-3 – volume: 255 start-page: 978 issue: 5 year: 2013 ident: 422_CR5 publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2013.05.001 – volume: 1962 start-page: 1 year: 1962 ident: 422_CR36 publication-title: Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II – volume: 95 start-page: 117 issue: 1–4 year: 2006 ident: 422_CR12 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-005-6215-x – volume: 41 start-page: 174 year: 1990 ident: 422_CR9 publication-title: Z. Angew. Math. Physik doi: 10.1007/BF00945107 – volume: 64 start-page: 261 issue: 3 year: 1996 ident: 422_CR15 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00728351 – volume: 18 start-page: 1705 issue: 4 year: 2005 ident: 422_CR25 publication-title: Nonlinearity doi: 10.1088/0951-7715/18/4/017 – volume: 31 start-page: 185 year: 1918 ident: 422_CR27 publication-title: Astron. J. doi: 10.1086/104299 – ident: 422_CR1 doi: 10.1007/s10569-024-10205-3 – volume: 49 start-page: 347 issue: 4 year: 1990 ident: 422_CR35 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00049444 – volume: 127 year: 2023 ident: 422_CR14 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2023.107556 – volume: 78 start-page: 17 year: 2000 ident: 422_CR29 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1023/A:1011187405509 – ident: 422_CR33 – volume: 78 start-page: 47 year: 2000 ident: 422_CR34 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1023/A:1011139523256 – volume: 3 start-page: 49 issue: 1 year: 1966 ident: 422_CR26 publication-title: Bull. Astron. – volume: 169 start-page: 136 year: 1967 ident: 422_CR37 publication-title: Math. Ann. doi: 10.1007/BF01399536 – ident: 422_CR24 doi: 10.1007/s10208-016-9339-3 – volume: 135 start-page: 44 issue: 4 year: 2023 ident: 422_CR40 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-023-10157-0 – ident: 422_CR10 doi: 10.1007/978-3-540-85146-2 – ident: 422_CR11 doi: 10.1007/978-3-642-61215-2_2 – volume: 18 start-page: 855 issue: 2 year: 2005 ident: 422_CR22 publication-title: Nonlinearity doi: 10.1088/0951-7715/18/2/020 – volume: 41 start-page: 453 issue: 4 year: 1990 ident: 422_CR8 publication-title: Z. Angew. Math. Physik doi: 10.1007/BF00945951 – volume: 98 start-page: 2 year: 1954 ident: 422_CR31 publication-title: Dokl. Akad. Nauk. SSR – volume: 178 start-page: 4 issue: 1 year: 2005 ident: 422_CR39 publication-title: Icarus doi: 10.1016/j.icarus.2005.03.017 – volume: 38 start-page: 565 issue: 4 year: 1996 ident: 422_CR30 publication-title: SIAM Rev. doi: 10.1137/S0036144595284180 |
| SSID | ssj0001138797 |
| Score | 2.34333 |
| Snippet | Perturbation theory is a very useful tool to investigate the dynamics of models in space science. We start by presenting some results obtained implementing... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Index Database |
| StartPage | 149 |
| SubjectTerms | Celestial mechanics Machine learning Orbital mechanics Perturbation theory Space debris Spacecraft breakup |
| Title | From perturbative methods to machine learning techniques in space science |
| URI | https://www.proquest.com/docview/3172759526 |
| Volume | 18 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVLSH databaseName: SpringerLink Journals customDbUrl: mediaType: online eissn: 2198-2759 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001138797 issn: 1972-6724 databaseCode: AFBBN dateStart: 20140301 isFulltext: true providerName: Library Specific Holdings – providerCode: PRVAVX databaseName: SpringerLINK - Czech Republic Consortium customDbUrl: eissn: 2198-2759 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001138797 issn: 1972-6724 databaseCode: AGYKE dateStart: 20140101 isFulltext: true titleUrlDefault: http://link.springer.com providerName: Springer Nature |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Nb9QwELVge4ED4lMUCvIBcVm5chzHTo4V6lKgLZdUWk6W43gRh-4u3SBV_fWdsZ2kq0UIuESRV9oonufxZDzzHiHvrG5lUSlYSNxLJr1VrFFNy4T3ALBWNtpig_PZuTq5kJ_nxXzU2AzdJV1z6G5-21fyP1aFMbArdsn-g2WHP4UBuAf7whUsDNe_svEMe0PW_gq2jSYSeEdB6MDacBnKJH2vC_F9OtC1hhJY8CTILhuX9tbRLqYSsBp6NW2xNArD0tUS61wT5bOdotAIwMpieIqVDX06IWUPRDGWT21lD7E0Gg8shu6W4AwrLZjSscf50IcxcHBgA51YvHc86ICU6A6zSEeadtYs6qvsOO1Yp7HB0FEyiBlYICZj1-MW1R_Ln381s4vTU1Mfz-v3658MxcPwkD0pqdwne0IrJSZk7-jjty93km1ZXuootNO_U2qgCm2UO0_eDlK29-gQeNSPyaP0xUCPovmfkHt--ZQ8PBvodjfPyCcEAr0LBJqAQLsVTUCgPRDoCAT6Y0kDEGgCwnNSz47rDycsaWQwJzTvWNFKmyuuXVsKm_MW4u3K561zmasWbeN4AR8kucUCN9-oKrMo384V98JB4F3lL8hkCRh6SahTXlrFc6-KBm6qUixkmXtfassX1i32ybSfE7OOTChm4LwOM2hgBk2YQXO9Tw76aTNpxWxMjtFyURVCvfrzz6_JgxGsB2TSXf3ybyD465q3ybS3HndbDA |
| linkProvider | Springer Nature |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=From+perturbative+methods+to+machine+learning+techniques+in+space+science&rft.jtitle=Bollettino+della+Unione+matematica+italiana+%282008%29&rft.date=2025-03-01&rft.pub=Springer+Nature+B.V&rft.issn=1972-6724&rft.eissn=2198-2759&rft.volume=18&rft.issue=1&rft.spage=149&rft.epage=166&rft_id=info:doi/10.1007%2Fs40574-024-00422-x&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1972-6724&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1972-6724&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1972-6724&client=summon |