Revisiting Hansen’s Ideal Frame Propagation with Special Perturbations—1: Basic Algorithms for Osculating Elements
A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known t...
Saved in:
| Published in | Universe (Basel) Vol. 9; no. 11; p. 470 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.11.2023
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2218-1997 2218-1997 |
| DOI | 10.3390/universe9110470 |
Cover
| Abstract | A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge. |
|---|---|
| AbstractList | A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge. |
| Audience | Academic |
| Author | Lara, Martin Urrutxua, Hodei |
| Author_xml | – sequence: 1 givenname: Martin orcidid: 0000-0001-6754-916X surname: Lara fullname: Lara, Martin – sequence: 2 givenname: Hodei orcidid: 0000-0002-9173-9593 surname: Urrutxua fullname: Urrutxua, Hodei |
| BookMark | eNqFUU1v3CAUtKpUaprm3CtSz5sAhgX3to2SZqVIifpxtp7xw2Vlgwv2RrnlR_TSv5dfUrKuqqqXigPw3swwj3ldHPngsSjeMnpWlhU9n73bY0xYMUaFoi-KY86ZXrGqUkd_nV8VpyntKKVMyXzVx8X-E-5dcpPzHbkGn9A_Pf5MZNsi9OQqwoDkLoYROphc8OTeTd_I5xGNy-07jNMcm0MnPT3-YO_JB0jOkE3fhZiRQyI2RHKbzNzD4YnLHgf0U3pTvLTQJzz9vZ8UX68uv1xcr25uP24vNjcrU66raSUpMGNl2wilkBqLDTOSScokawWoPKwRXEsq8idUmivRMM44F0asW6lRlifFdtFtA-zqMboB4kMdwNWHQohdDXFypseaCi1U1bDWoBXSchAlW0NlRak1l0pkLbpozX6Eh3vo-z-CjNbPMdT_xJAp7xbKGMP3GdNU78IcfZ645roqSyqFfkadLagOsg_nbZgimLxaHJzJQVuX6xuVPai1pioTzheCiSGliPa_Rn4BndSsLA |
| Cites_doi | 10.2514/2.4654 10.2514/1.G002753 10.1515/9783110668513 10.1016/j.asr.2022.04.007 10.1080/00029890.1983.11971232 10.1103/PhysRevLett.107.181101 10.2514/6.1974-838 10.1007/BF01230743 10.1007/s10569-011-9396-5 10.1007/BF01231274 10.1007/BF01229950 10.1007/BF01229192 10.3934/jgm.2010.2.223 10.1007/BF02418577 10.1515/crll.1965.218.204 10.1007/978-94-009-6487-7 10.1007/BF01235849 10.1007/BF00645273 10.1007/s10569-011-9368-9 10.1007/978-3-642-46319-8 10.1007/BF01231102 10.1007/BF00692474 10.1002/asna.18520332602 10.1007/BF00691913 10.1007/s10569-015-9647-y 10.1086/106836 10.1007/BF01229551 10.1086/108598 10.1086/108597 10.1111/j.1365-2966.2005.09658.x 10.1007/s10569-013-9530-7 10.1007/BF01235121 10.1016/B978-0-12-395732-0.50016-7 10.1007/BF02422379 10.1007/BF01229494 10.1007/BF00058994 10.1086/319408 10.1007/978-3-642-88412-2 10.1196/annals.1370.026 10.1007/s10569-013-9475-x 10.1093/mnras/68.8.576 10.2514/1.32237 10.1007/BF00050714 10.1007/s10569-019-9887-3 10.1093/mnras/stv2106 10.1119/1.12522 10.1007/BF01371329 10.1088/0305-4470/28/22/015 10.1007/978-3-319-23986-6_11 10.1088/0004-6256/148/3/43 10.1007/BF01247138 10.2514/3.5597 10.1051/0004-6361/201937106 10.1086/509606 10.1016/0370-2693(81)90372-5 10.1017/S0305004100037336 10.1007/BF01229118 10.1007/s10569-006-9056-3 10.1007/BF01229552 10.1016/0771-050X(80)90013-3 10.2514/3.5268 10.1086/107009 10.1007/BF01390175 10.1007/BF01229287 10.1007/BF01232657 10.1007/BF01227757 10.1515/9783110559125 10.1007/978-3-642-65027-7 10.1007/BF00051816 10.1007/BF00695790 10.1007/BF01601478 10.1007/BF01232728 10.1086/103991 10.1093/qjmam/15.3.283 10.2514/3.19847 10.4171/OWR/2006/14 10.1007/s10569-017-9770-z 10.1086/108202 10.1016/j.mcm.2007.07.010 10.1029/JZ064i012p02271 10.1007/s10569-019-9897-1 10.1007/BF01231123 10.1007/BF01228432 10.1007/BF01235123 10.1007/BF00056354 10.1086/423039 |
| ContentType | Journal Article |
| Copyright | COPYRIGHT 2023 MDPI AG 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. |
| Copyright_xml | – notice: COPYRIGHT 2023 MDPI AG – notice: 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. |
| DBID | AAYXX CITATION ABUWG AFKRA AZQEC BENPR BHPHI BKSAR CCPQU DWQXO HCIFZ PCBAR PHGZM PHGZT PIMPY PKEHL PQEST PQQKQ PQUKI PRINS ADTOC UNPAY DOA |
| DOI | 10.3390/universe9110470 |
| DatabaseName | CrossRef ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central (subscription) Natural Science Collection Earth, Atmospheric & Aquatic Science Collection ProQuest One Community College ProQuest Central Korea SciTech Premium Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Unpaywall for CDI: Periodical Content Unpaywall DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China Earth, Atmospheric & Aquatic Science Collection ProQuest Central ProQuest One Academic UKI Edition Natural Science Collection ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Publicly Available Content Database CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository – sequence: 3 dbid: BENPR name: ProQuest Central url: http://www.proquest.com/pqcentral?accountid=15518 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2218-1997 |
| ExternalDocumentID | oai_doaj_org_article_048479b1dcef45f2a4316a9f43882574 10.3390/universe9110470 A774376807 10_3390_universe9110470 |
| GeographicLocations | United Kingdom Germany Spain |
| GeographicLocations_xml | – name: United Kingdom – name: Spain – name: Germany |
| GroupedDBID | 5VS 8FE 8FH AADQD AAFWJ AAYXX ABDBF ADBBV AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS BCNDV BENPR BHPHI BKSAR CCPQU CITATION GROUPED_DOAJ HCIFZ IAO ITC KQ8 LK5 M7R MODMG M~E OK1 PCBAR PHGZM PHGZT PIMPY PROAC ABUWG AZQEC DWQXO PKEHL PQEST PQQKQ PQUKI PRINS ADTOC IPNFZ RIG UNPAY |
| ID | FETCH-LOGICAL-c369t-50a1cf5db477e0cfeb1c5150151d4a7110c42850433998274b121224c46d58e53 |
| IEDL.DBID | DOA |
| ISSN | 2218-1997 |
| IngestDate | Fri Oct 03 12:53:44 EDT 2025 Sun Oct 26 04:07:41 EDT 2025 Mon Jun 30 11:30:08 EDT 2025 Mon Oct 20 17:12:16 EDT 2025 Thu Oct 16 04:41:13 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Language | English |
| License | cc-by |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c369t-50a1cf5db477e0cfeb1c5150151d4a7110c42850433998274b121224c46d58e53 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-6754-916X 0000-0002-9173-9593 |
| OpenAccessLink | https://doaj.org/article/048479b1dcef45f2a4316a9f43882574 |
| PQID | 2893305480 |
| PQPubID | 2059542 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_048479b1dcef45f2a4316a9f43882574 unpaywall_primary_10_3390_universe9110470 proquest_journals_2893305480 gale_infotracacademiconefile_A774376807 crossref_primary_10_3390_universe9110470 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-11-01 |
| PublicationDateYYYYMMDD | 2023-11-01 |
| PublicationDate_xml | – month: 11 year: 2023 text: 2023-11-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Universe (Basel) |
| PublicationYear | 2023 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Kamel (ref_37) 1983; 6 Ferrandiz (ref_51) 1992; 53 Cayley (ref_95) 1890; Volume III Herrick (ref_16) 1953; 58 Ferrer (ref_79) 1987; 40 Urrutxua (ref_66) 2016; 124 Shefer (ref_50) 1990; 49 ref_10 ref_98 Baumgarte (ref_112) 1976; 14 ref_96 Vittaldev (ref_101) 2012; 112 Palacios (ref_63) 1996; 44 Sundman (ref_67) 1913; 36 Rosengren (ref_27) 2014; 118 Nacozy (ref_36) 1977; 16 ref_15 Barrio (ref_49) 2008; 48 Urrutxua (ref_44) 2016; 158 Breiter (ref_58) 2019; 131 Musen (ref_17) 1954; 59 Deprit (ref_72) 1994; 58 Milnor (ref_97) 1983; 90 ref_23 Cowell (ref_3) 1910; 71 ref_29 Broucke (ref_12) 1972; 5 Floria (ref_120) 1995; 28 Tapley (ref_74) 1967; 4 (ref_14) 1929; 65 Andoyer (ref_121) 1913; 30 ref_71 Kustaanheimo (ref_5) 1965; 1965 Breiter (ref_24) 2005; 364 Roa (ref_57) 2017; 40 Fukushima (ref_40) 2007; 133 Sperling (ref_34) 1961; 31 ref_83 ref_80 Hill (ref_124) 1913; 27 Leubner (ref_106) 1981; 49 Deprit (ref_108) 1970; 2 Tapley (ref_75) 1969; 7 Ferrer (ref_41) 2010; 2 Szebehely (ref_38) 1983; 30 ref_88 Ferrandiz (ref_7) 1986; Volume 255 ref_84 Hintz (ref_13) 2008; 31 Lara (ref_45) 2022; 69 Arsenault (ref_11) 1970; 8 Herget (ref_18) 1962; 67 Scheifele (ref_87) 1970; 271 Altman (ref_99) 1972; 6 Hansen (ref_53) 1857; 5 Alfriend (ref_115) 1977; 16 Amato (ref_59) 2019; 131 McGehee (ref_76) 1974; 27 Dormand (ref_32) 1980; 6 (ref_116) 1981; 98 Hunt (ref_62) 1991; Volume 326 Scheifele (ref_77) 1970; 2 Shuster (ref_61) 1993; 41 Bombardelli (ref_90) 2014; 148 Lara (ref_82) 2017; 129 Allan (ref_19) 1962; 15 Roy (ref_21) 1973; 7 Fukushima (ref_46) 2005; 1065 (ref_110) 2000; 23 Lara (ref_28) 2020; 634 ref_60 Deprit (ref_22) 1975; 79 Bond (ref_119) 1981; 23 ref_68 Allan (ref_20) 1963; 59 Flury (ref_125) 1975; 36 ref_64 Garofalo (ref_102) 1960; 65 Broucke (ref_55) 1971; 13 (ref_8) 1988; 41 Deprit (ref_56) 1976; 13 Cohen (ref_81) 1962; 67 (ref_52) 1995; 63 Bombardelli (ref_65) 2013; 116 Scheifele (ref_89) 1981; Volume 160 Vitins (ref_91) 1978; 17 Bond (ref_123) 1980; 21 Correia (ref_25) 2011; 111 ref_114 ref_117 ref_118 Velez (ref_73) 1974; 10 Bohlin (ref_70) 1911; 28 ref_33 ref_111 ref_31 ref_30 Katz (ref_26) 2011; 107 Cowell (ref_2) 1908; 68 Arakida (ref_86) 2001; 121 Burdet (ref_35) 1968; 19 (ref_69) 1906; 30 ref_105 Masdemont (ref_94) 2016; Volume 44 Deprit (ref_92) 1981; 24 ref_47 Fukushima (ref_48) 2004; 128 (ref_93) 1993; 57 Nacozy (ref_85) 1981; 23 ref_100 ref_42 Lara (ref_104) 2014; 150 Sharaf (ref_39) 1992; 56 Deprit (ref_122) 1981; 23 Bombardelli (ref_113) 2015; 454 Sharaf (ref_109) 1991; 55 Hedo (ref_107) 2007; 97 ref_9 Ferrandiz (ref_78) 1986; 37 Stiefel (ref_43) 1970; 2 ref_4 Alfriend (ref_103) 1984; 32 Encke (ref_1) 1852; 33 ref_6 Musen (ref_54) 1959; 64 |
| References_xml | – ident: ref_117 – ident: ref_9 – volume: 23 start-page: 1085 year: 2000 ident: ref_110 article-title: New Method for Extracting the Quaternion from a Rotation Matrix publication-title: J. Guid. Control Dyn. doi: 10.2514/2.4654 – volume: 40 start-page: 2737 year: 2017 ident: ref_57 article-title: Alternative Set of Nonsingular Quaternionic Orbital Elements publication-title: J. Guid. Control Dyn. doi: 10.2514/1.G002753 – ident: ref_100 – volume: Volume 160 start-page: 299 year: 1981 ident: ref_89 article-title: An analytical singularity-free orbit predictor for near-earth satellites publication-title: Proceedings of the International Symposium on Spacecraft Flight Dynamics – ident: ref_114 doi: 10.1515/9783110668513 – volume: 5 start-page: 41 year: 1857 ident: ref_53 article-title: Auseinandersetzung einer zweckmässigen Methode zur Berechnung der absoluten Störungen der kleinen Planeten. Erste Abhandlung publication-title: Abh. Der K. Sachs. Ges. Der Wiss. – volume: 69 start-page: 4169 year: 2022 ident: ref_45 article-title: Note on the analytical integration of circumterrestrial orbits publication-title: Adv. Space Res. doi: 10.1016/j.asr.2022.04.007 – volume: 90 start-page: 353 year: 1983 ident: ref_97 article-title: On the Geometry of the Kepler Problem publication-title: Am. Math. Mon. doi: 10.1080/00029890.1983.11971232 – ident: ref_88 – volume: 107 start-page: 181101 year: 2011 ident: ref_26 article-title: Long-Term Cycling of Kozai-Lidov Cycles: Extreme Eccentricities and Inclinations Excited by a Distant Eccentric Perturber publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.107.181101 – ident: ref_80 doi: 10.2514/6.1974-838 – ident: ref_71 – volume: 23 start-page: 299 year: 1981 ident: ref_122 article-title: A Note Concerning the TR-Transformation publication-title: Celest. Mech. doi: 10.1007/BF01230743 – volume: 112 start-page: 253 year: 2012 ident: ref_101 article-title: Unified State Model theory and application in Astrodynamics publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-011-9396-5 – volume: 28 start-page: 113 year: 1911 ident: ref_70 article-title: Note sur le problème des deux corps et sur une intégration nouvelle dans le problème des trois corps publication-title: Bull. Astron. Ser. I – volume: 21 start-page: 357 year: 1980 ident: ref_123 article-title: Analytical Satellite Theory in Extended Phase Space publication-title: Celest. Mech. doi: 10.1007/BF01231274 – ident: ref_4 – ident: ref_31 – volume: Volume 326 start-page: 65 year: 1991 ident: ref_62 article-title: An efficient formulation for numerical orbit computation publication-title: ESA, Spacecraft Flight Dynamics – ident: ref_10 – volume: 158 start-page: 2503 year: 2016 ident: ref_44 article-title: Impact of the integration stop-condition on the accuracy of regularized orbit formulations (AAS 16-353) publication-title: Adv. Astronaut. Sci. – ident: ref_83 – volume: 7 start-page: 236 year: 1973 ident: ref_21 article-title: Studies in the Application of Recurrence Relations to Special Perturbation Methods. III. Non-Singular Differential Equations for Special Perturbations publication-title: Celest. Mech. doi: 10.1007/BF01229950 – volume: 24 start-page: 111 year: 1981 ident: ref_92 article-title: The elimination of the parallax in satellite theory publication-title: Celest. Mech. doi: 10.1007/BF01229192 – volume: 2 start-page: 223 year: 2010 ident: ref_41 article-title: Families of Canonical Transformations by Hamilton-Jacobi-Poincaré Equation. Application to Rotational and Orbital Motion publication-title: J. Geom. Mech. doi: 10.3934/jgm.2010.2.223 – volume: 41 start-page: 439 year: 1993 ident: ref_61 article-title: A Survey of Attitude Representations publication-title: J. Astronaut. Sci. – volume: 30 start-page: 305 year: 1906 ident: ref_69 article-title: Sur la résolution qualitative du problème restreint des trois corps publication-title: Acta Math. doi: 10.1007/BF02418577 – volume: 4 start-page: 5 year: 1967 ident: ref_74 article-title: The Regularization of Optimal Trajectories publication-title: JPL Space Programs Summ. – volume: 1965 start-page: 204 year: 1965 ident: ref_5 article-title: Perturbation theory of Kepler motion based on spinor regularization publication-title: J. Für Die Reine Und Angew. Math. (Crelles J.) doi: 10.1515/crll.1965.218.204 – ident: ref_30 – ident: ref_23 doi: 10.1007/978-94-009-6487-7 – volume: 40 start-page: 315 year: 1987 ident: ref_79 article-title: Generalized Elliptic Anomalies publication-title: Celest. Mech. doi: 10.1007/BF01235849 – volume: 36 start-page: 495 year: 1975 ident: ref_125 article-title: Accurate Integration of Geostationary Orbits with Burdet’s Focal Elements publication-title: Astrophys. Space Sci. doi: 10.1007/BF00645273 – volume: 111 start-page: 105 year: 2011 ident: ref_25 article-title: Tidal evolution of hierarchical and inclined systems publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-011-9368-9 – ident: ref_84 doi: 10.1007/978-3-642-46319-8 – volume: 30 start-page: 59 year: 1983 ident: ref_38 article-title: Transformations of the Perturbed Two-Body Problem to Unperturbed Harmonic Oscillators publication-title: Celest. Mech. doi: 10.1007/BF01231102 – volume: 57 start-page: 203 year: 1993 ident: ref_93 article-title: Canonical elements and Keplerian-like solutions for intermediary orbits of satellites of an oblate planet publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00692474 – volume: 13 start-page: 390 year: 1971 ident: ref_55 article-title: Redundant Variables in Celestial Mechanics publication-title: Astron. Astrophys. – volume: 33 start-page: 377 year: 1852 ident: ref_1 article-title: Über eine neue Methode der Berechnung der Planetenstörungen von J. F. Encke publication-title: Astron. Nachrichten doi: 10.1002/asna.18520332602 – volume: 63 start-page: 29 year: 1995 ident: ref_52 article-title: Behaviour of the SMF Method for the Numerical Integration of Satellite Orbits publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00691913 – volume: 124 start-page: 1 year: 2016 ident: ref_66 article-title: DROMO propagator revisited publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-015-9647-y – volume: 58 start-page: 156 year: 1953 ident: ref_16 article-title: Icarus and the variation of parameters publication-title: Astron. J. doi: 10.1086/106836 – ident: ref_33 – volume: Volume 255 start-page: 361 year: 1986 ident: ref_7 article-title: A new set of canonical variables for orbit calculations publication-title: ESA Proceedings of the Second International Symposium on Spacecraft Flight Dynamics – volume: 23 start-page: 159 year: 1981 ident: ref_119 article-title: Canonical Orbital Elements in Terms of an Arbitrary Independent Variable publication-title: Celest. Mech. doi: 10.1007/BF01229551 – volume: 67 start-page: 16 year: 1962 ident: ref_18 article-title: On the variation of arbitrary vectorial constants publication-title: Astron. J. doi: 10.1086/108598 – ident: ref_64 – volume: 67 start-page: 10 year: 1962 ident: ref_81 article-title: A nonsingular set of orbit elements publication-title: Astron. J. doi: 10.1086/108597 – volume: 364 start-page: 1222 year: 2005 ident: ref_24 article-title: Vectorial elements for the Galactic disc tide effects in cometary motion publication-title: Mon. Not. R. Astron. Soc. doi: 10.1111/j.1365-2966.2005.09658.x – volume: 118 start-page: 197 year: 2014 ident: ref_27 article-title: On the Milankovitch orbital elements for perturbed Keplerian motion publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-013-9530-7 – volume: 2 start-page: 274 year: 1970 ident: ref_43 article-title: Remarks on Numerical Integration of Keplerian Orbits publication-title: Celest. Mech. doi: 10.1007/BF01235121 – ident: ref_68 doi: 10.1016/B978-0-12-395732-0.50016-7 – volume: 36 start-page: 105 year: 1913 ident: ref_67 article-title: Mémoire sur le problème des trois corps publication-title: Acta Math. doi: 10.1007/BF02422379 – volume: 2 start-page: 166 year: 1970 ident: ref_108 article-title: The Main Problem of Artificial Satellite Theory for Small and Moderate Eccentricities publication-title: Celest. Mech. doi: 10.1007/BF01229494 – volume: 55 start-page: 21 year: 1991 ident: ref_109 article-title: The Motion of Artificial Satellites in the Set of Eulerian Redundant Parameters publication-title: Earth Moon Planets doi: 10.1007/BF00058994 – volume: 121 start-page: 1764 year: 2001 ident: ref_86 article-title: Long-Term Integration Error of Kustaanheimo-Stiefel Regularized Orbital Motion. II. Method of Variation of Parameters publication-title: Astron. J. doi: 10.1086/319408 – ident: ref_105 doi: 10.1007/978-3-642-88412-2 – volume: 1065 start-page: 37 year: 2005 ident: ref_46 article-title: Efficient Orbit Integration by Manifold Correction Methods publication-title: Ann. N. Y. Acad. Sci. doi: 10.1196/annals.1370.026 – volume: 71 start-page: 1 year: 1910 ident: ref_3 article-title: Investigation of the Motion of Halley’s Comet From 1759 to 1910 publication-title: Greenwich Obs. Astron. Magn. Meteorol. Made R. Obs. Ser. 2 – volume: 116 start-page: 53 year: 2013 ident: ref_65 article-title: A new set of integrals of motion to propagate the perturbed two-body problem publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-013-9475-x – volume: 68 start-page: 576 year: 1908 ident: ref_2 article-title: The Orbit of Jupiter’s Eighth Satellite publication-title: Mon. Not. R. Astron. Soc. doi: 10.1093/mnras/68.8.576 – volume: 31 start-page: 785 year: 2008 ident: ref_13 article-title: Survey of Orbit Element Sets publication-title: J. Guid. Control Dyn. doi: 10.2514/1.32237 – ident: ref_98 – volume: 31 start-page: 660 year: 1961 ident: ref_34 article-title: Computation of Keplerian Conic Sections publication-title: ARS J. – volume: 49 start-page: 197 year: 1990 ident: ref_50 article-title: Application of KS-transformation in the problem of investigation of the motion of unusual minor planets and comets publication-title: Celest. Mech. doi: 10.1007/BF00050714 – volume: 131 start-page: 9 year: 2019 ident: ref_58 article-title: The Lissajous-Kustaanheimo-Stiefel transformation publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-019-9887-3 – volume: 454 start-page: 2890 year: 2015 ident: ref_113 article-title: Non-singular orbital elements for special perturbations in the two-body problem publication-title: Mon. Not. R. Astron. Soc. doi: 10.1093/mnras/stv2106 – volume: 44 start-page: 63 year: 1996 ident: ref_63 article-title: Ideal frames and regularization in numerical orbit computation publication-title: J. Astronaut. Sci. – volume: 49 start-page: 232 year: 1981 ident: ref_106 article-title: Correcting a widespread error concerning the angular velocity of a rotating rigid body publication-title: Am. J. Phys. doi: 10.1119/1.12522 – ident: ref_118 – volume: 17 start-page: 173 year: 1978 ident: ref_91 article-title: Keplerian Motion and Gyration publication-title: Celest. Mech. doi: 10.1007/BF01371329 – volume: 28 start-page: 6395 year: 1995 ident: ref_120 article-title: A universal approach to the intermediate anomaly of Keplerian motion publication-title: J. Phys. A Math. Gen. doi: 10.1088/0305-4470/28/22/015 – volume: 79 start-page: 1 year: 1975 ident: ref_22 article-title: Ideal elements for perturbed Keplerian motions publication-title: J. Res. Natl. Bur. Stand. – volume: Volume 44 start-page: 151 year: 2016 ident: ref_94 article-title: Analytical and Semianalytical Propagation of Space Orbits: The Role of Polar-Nodal Variables publication-title: Astrodynamics Network AstroNet-II. Astrophysics and Space Science Proceedings doi: 10.1007/978-3-319-23986-6_11 – volume: 148 start-page: 43 year: 2014 ident: ref_90 article-title: Time Elements for Enhanced Performance of the Dromo Orbit Propagator publication-title: Astron. J. doi: 10.1088/0004-6256/148/3/43 – volume: 14 start-page: 121 year: 1976 ident: ref_112 article-title: A New Time Element for A General Time Transformation publication-title: Celest. Mech. doi: 10.1007/BF01247138 – volume: 8 start-page: 4 year: 1970 ident: ref_11 article-title: Orbit determination using analytic partial derivatives of perturbed motion publication-title: AIAA J. doi: 10.2514/3.5597 – volume: 634 start-page: 1 year: 2020 ident: ref_28 article-title: Non-singular recursion formulas for third-body perturbations in mean vectorial elements publication-title: Astron. Astrophys. doi: 10.1051/0004-6361/201937106 – volume: 133 start-page: 1 year: 2007 ident: ref_40 article-title: New Two-Body Regularization publication-title: Astron. J. doi: 10.1086/509606 – volume: 98 start-page: 77 year: 1981 ident: ref_116 article-title: Weakly canonical transformations and the path integral quantization publication-title: Phys. Lett. B doi: 10.1016/0370-2693(81)90372-5 – volume: 59 start-page: 669 year: 1963 ident: ref_20 article-title: Planetary equations in terms of vectorial elements publication-title: Proc. Camb. Philos. Soc. doi: 10.1017/S0305004100037336 – volume: 10 start-page: 405 year: 1974 ident: ref_73 article-title: Notions of Analytic Vs Numerical Stability as Applied to the Numerical Calculation of Orbits publication-title: Celest. Mech. doi: 10.1007/BF01229118 – volume: 97 start-page: 131 year: 2007 ident: ref_107 article-title: A special perturbation method in orbital dynamics publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-006-9056-3 – volume: 23 start-page: 173 year: 1981 ident: ref_85 article-title: Time Elements in Keplerian Orbital Elements publication-title: Celest. Mech. doi: 10.1007/BF01229552 – volume: 6 start-page: 19 year: 1980 ident: ref_32 article-title: A family of embedded Runge-Kutta formulae publication-title: J. Comput. Appl. Math. doi: 10.1016/0771-050X(80)90013-3 – volume: 7 start-page: 1010 year: 1969 ident: ref_75 article-title: Trajectory optimization using regularized variables publication-title: AIAA J. doi: 10.2514/3.5268 – volume: 59 start-page: 262 year: 1954 ident: ref_17 article-title: Special perturbations of the vectorial elements publication-title: Astron. J. doi: 10.1086/107009 – volume: 271 start-page: 729 year: 1970 ident: ref_87 article-title: Généralisation des éléments de Delaunay en mécanique céleste. Application au mouvement d’un satellite artificiel publication-title: Acad. Des Sci. Paris C. R. Ser. B Sci. Phys. – volume: 37 start-page: 226 year: 1986 ident: ref_78 article-title: A New Integrated, General Time Transformation in the Kepler Problem publication-title: Bull. Astron. Inst. Czechoslov. – volume: 27 start-page: 191 year: 1974 ident: ref_76 article-title: Triple collision in the collinear three-body problem publication-title: Invent. Math. doi: 10.1007/BF01390175 – volume: 65 start-page: 1 year: 1929 ident: ref_14 article-title: Formeln zur genaeherten Stoerungsrechnung in Bahnelementen. Angewandt auf die Planeten 633 Zelima, 956 [1921 IW], 979 Ilsewa, 1035 Amata und 1049 [1925RB] publication-title: Publ. Og Mindre Meddeler Fra Kobenhavns Obs. – volume: 16 start-page: 441 year: 1977 ident: ref_115 article-title: The extended phase space formulation of the Vinti problem publication-title: Celest. Mech. doi: 10.1007/BF01229287 – volume: 16 start-page: 309 year: 1977 ident: ref_36 article-title: The Intermediate Anomaly publication-title: Celest. Mech. doi: 10.1007/BF01232657 – volume: 6 start-page: 425 year: 1972 ident: ref_99 article-title: A Unified State Model of Orbital Trajectory and Attitude Dynamics publication-title: Celest. Mech. doi: 10.1007/BF01227757 – volume: 150 start-page: 315 year: 2014 ident: ref_104 article-title: Proper Averaging Via Parallax Elimination (AAS 13-722) publication-title: Adv. Astronaut. Sci. – ident: ref_42 doi: 10.1515/9783110559125 – ident: ref_6 doi: 10.1007/978-3-642-65027-7 – volume: 53 start-page: 347 year: 1992 ident: ref_51 article-title: Increased Accuracy of Computations in the Main Satellite Problem through Linearization Methods publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00051816 – volume: 58 start-page: 151 year: 1994 ident: ref_72 article-title: Linearization: Laplace vs. Stiefel publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/BF00695790 – volume: 19 start-page: 345 year: 1968 ident: ref_35 article-title: Theory of Kepler motion: The general perturbed two body problem publication-title: Z. Angew. Math. Und Phys. doi: 10.1007/BF01601478 – volume: 13 start-page: 253 year: 1976 ident: ref_56 article-title: Ideal Frames for Perturbed Keplerian Motions publication-title: Celest. Mech. doi: 10.1007/BF01232728 – ident: ref_111 – ident: ref_96 – volume: 27 start-page: 171 year: 1913 ident: ref_124 article-title: Motion of a system of material points under the action of gravitation publication-title: Astron. J. doi: 10.1086/103991 – volume: 15 start-page: 283 year: 1962 ident: ref_19 article-title: Satellite orbit perturbations due to radiation pressure and luni-solar forces publication-title: Q. J. Mech. Appl. Math. doi: 10.1093/qjmam/15.3.283 – volume: 6 start-page: 387 year: 1983 ident: ref_37 article-title: New nonsingular forms of perturbed satellite equations of motion publication-title: J. Guid. Control Dyn. doi: 10.2514/3.19847 – ident: ref_47 doi: 10.4171/OWR/2006/14 – volume: 129 start-page: 137 year: 2017 ident: ref_82 article-title: Note on the ideal frame formulation publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-017-9770-z – volume: 65 start-page: 117 year: 1960 ident: ref_102 article-title: New set of variables for astronomical problems publication-title: Astron. J. doi: 10.1086/108202 – volume: 48 start-page: 594 year: 2008 ident: ref_49 article-title: Performance of perturbation methods on orbit prediction publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2007.07.010 – volume: 64 start-page: 2271 year: 1959 ident: ref_54 article-title: Application of Hansen’s theory to the motion of an artificial satellite in the gravitational field of the Earth publication-title: J. Geophys. Res. doi: 10.1029/JZ064i012p02271 – volume: 131 start-page: 21 year: 2019 ident: ref_59 article-title: Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-019-9897-1 – volume: 32 start-page: 163 year: 1984 ident: ref_103 article-title: Elimination of the perigee in the satellite problem publication-title: Celest. Mech. doi: 10.1007/BF01231123 – ident: ref_29 – volume: 5 start-page: 303 year: 1972 ident: ref_12 article-title: On the Equinoctial Orbit Elements publication-title: Celest. Mech. doi: 10.1007/BF01228432 – volume: 41 start-page: 343 year: 1988 ident: ref_8 article-title: A general canonical transformation increasing the number of variables with application to the two-body problem publication-title: Celest. Mech. – volume: 2 start-page: 296 year: 1970 ident: ref_77 article-title: On Nonclassical Canonical Systems publication-title: Celest. Mech. doi: 10.1007/BF01235123 – volume: Volume III start-page: 13 year: 1890 ident: ref_95 article-title: On Hansen’s lunar theory publication-title: Collected Mathematical Works – volume: 30 start-page: 425 year: 1913 ident: ref_121 article-title: Sur l’anomalie excentrique et l’anomalie vraie comme éléments canoniques du mouvement eliptique, d’après MM. T. Levi-Civita et G.-W. Hill publication-title: Bull. Astron. Ser. I – ident: ref_15 – volume: 56 start-page: 141 year: 1992 ident: ref_39 article-title: Motion of artificial satellites in the set of Eulerian redundant parameters (III) publication-title: Earth Moon Planets doi: 10.1007/BF00056354 – volume: 128 start-page: 1446 year: 2004 ident: ref_48 article-title: Further Simplification of the Manifold Correction Method for Orbit Integration publication-title: Astron. J. doi: 10.1086/423039 – ident: ref_60 |
| SSID | ssj0001759978 |
| Score | 2.246323 |
| SecondaryResourceType | review_article |
| Snippet | A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental... |
| SourceID | doaj unpaywall proquest gale crossref |
| SourceType | Open Website Open Access Repository Aggregation Database Index Database |
| StartPage | 470 |
| SubjectTerms | Algorithms Analysis Differential equations ideal elements ideal frames Mechanics orbit propagation Orbits perturbed Kepler motion Propagation time regularization Variables variation of parameters |
| SummonAdditionalLinks | – databaseName: ProQuest Central (subscription) dbid: BENPR link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwhV1Nb9NAEB2VVAg4IL4qDAXtAQk4WLXjXW-ChFCCEgUkQlRRqbfVej_CISTBdkDc-iO48Pf6S5hZ220FElytyLFmPLPzxjPvATxzwnot-zr2WTKIufUcQ0pg4Nk0cbLwXAa5tw_zfHbC35-K0z2Yd7swNFbZ5cSQqO3GUI_8qE-68Amxk73Zfo1JNYq-rnYSGrqVVrCvA8XYNdjvEzNWD_bHk_ni-LLrIsUQcVPD8ZMh3j_aNfMPDoM-4SRZfOV4Ciz-f-fqW3Bjt97qH9_1anXlMJregdttFclGjdvvwp5b34PrYZrTVPfh23HYGaeJZjbT1D0-P_tVsXcWq0I2pXEstigRLS-DWxj1YlkrRM8WrsRTqGgaeednP9NXbKzxtmy0WqI96s9fKoaFLvsYJljDX0yaEfTqAZxMJ5_ezuJWYCE2WT6sY5Ho1HhhCy6lS4zHvG2wvsEKIbVcS7SIQXQSOM4QlSF-LdCoeOYbnlsxcCI7gN56s3YPgRW5yGya-qzgCNmSREstilxr5zGBOZlH8KKzq9o2PBoK8Qe5QP3hggjGZPeLnxEBdriwKZeqjSeFiYfLYZFa4zwXvq9ppV8PPc8QMgjJI3hOXlMUpnWpjW63DfBpifBKjbDsxdw6SGQEh51jVRu_lbp82yJ4eeHs_z35o3_f6jHcJLH6ZpPxEHp1uXNPsKSpi6fte_obIb741w priority: 102 providerName: ProQuest – databaseName: Unpaywall dbid: UNPAY link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NbxMxELUgFQIOfCMCBfmABBy2a-_a64QLSlGjgESJEJHKyfJnhAhJtLspglN_BBf-Xn8JY69TVeWA4Bo5iZPxzLw3-zyD0FPHrVeiUJkvySBj1jNwKQ6OZylxQnsm4ri3d4fVZMbeHvGjVHBrkqwSqPjnGKQLyD9RCZEPc0pzJki-tv7Vcaok0QoIMyvBRS6jnYoDFu-hndnhdPQpTJTbvrfr51MCt883ndbBgYMTFsYTn0tFsWP_n3H5Orq6Wa7V929qsTiXeMY3kdxuudObfNnbtHrP_LjQzfH_f9MtdCNhUjzqDtFtdMkt76ArURtqmrvo-EO8gR700XiiQi369ORXg99YwJh4HMRdeFoD955HI-NQ2cVprD2euhpymu7KgqcnP-lLvK_gY_FoMV_VsPJrgwE24_dRDxu_4qATtDf30Gx88PH1JEvjGjJTVsM240RR47nVTAhHjIcsYAAtAd6glikB_7kBrhM7pgHHAzasaRGe6xlWWT5wvLyPesvV0j1AWFe8tJT6UjMggIQoobiulHIewqETVR8931pOrruuHBLYTDCyvGDkPtoPlj1bFtppxxdW9Vwm75QQxpgYamqN84z7QoUGAWroWQkEhAvWR8_CuZDB6dtaGZXuLsBuQ_ssOQIQDSYbENFHu9ujI1M0aCSQ2hLiKhvAbl6cHae_7fzhP6x9hK4VgL66S5K7qNfWG_cY0FKrnySX-A1zHBIS priority: 102 providerName: Unpaywall |
| Title | Revisiting Hansen’s Ideal Frame Propagation with Special Perturbations—1: Basic Algorithms for Osculating Elements |
| URI | https://www.proquest.com/docview/2893305480 https://www.mdpi.com/2218-1997/9/11/470/pdf?version=1698743376 https://doaj.org/article/048479b1dcef45f2a4316a9f43882574 |
| UnpaywallVersion | publishedVersion |
| Volume | 9 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAFT databaseName: Open Access Digital Library customDbUrl: eissn: 2218-1997 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001759978 issn: 2218-1997 databaseCode: KQ8 dateStart: 20150101 isFulltext: true titleUrlDefault: http://grweb.coalliance.org/oadl/oadl.html providerName: Colorado Alliance of Research Libraries – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2218-1997 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001759978 issn: 2218-1997 databaseCode: DOA dateStart: 20150101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVEBS databaseName: EBSCOhost Academic Search Ultimate customDbUrl: https://search.ebscohost.com/login.aspx?authtype=ip,shib&custid=s3936755&profile=ehost&defaultdb=asn eissn: 2218-1997 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001759978 issn: 2218-1997 databaseCode: ABDBF dateStart: 20211001 isFulltext: true titleUrlDefault: https://search.ebscohost.com/direct.asp?db=asn providerName: EBSCOhost – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2218-1997 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001759978 issn: 2218-1997 databaseCode: M~E dateStart: 20150101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: http://www.proquest.com/pqcentral?accountid=15518 eissn: 2218-1997 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001759978 issn: 2218-1997 databaseCode: BENPR dateStart: 20150601 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lb9QwEB6hIgQcEE-xUCofkIBDVGdjxwm3BHa1ILGsKlYqJ8vPXpZtleyCuPVHcOHv9ZcwttNqBYdeOEWJrGQ04xnPN5kHwEvHrVdirDJf0Cpj1jNUKY6KZ3PqhPZMxHFvn-blbMk-HvPjnVFfIScstQdOjDvEHcZErXNrnGfcj1Wo3Va1ZwX6hlzETqC0qnfAVIyuCF4jPkq9fArE9YfblOfgULkpC6OJd46h2K3_X5t8F25v12fq5w-1Wu0cOtP7cG_wFkmTqHwAN9z6IdyKWZumfwTfj2JteMhcJjMVosQX57978sGi90emIe2KLDpExSeR_STEXMkwcJ4sXIenjU4Bu4vzX_lb0ip8LWlWJ6cdrvzWE3RoyeeYqRo_MUmp5v1jWE4nX97NsmGQQmaKst5knKrceG41E8JR49E-G_Rj0BPILVMCOWIQhcReZoi-EKfqfBz-uBlWWl45XjyBvfXp2j0Fokte2Dz3hWYIzShVQnFdKuU8GionyhG8vuSrPEv9MiTijCAC-ZcIRtAGvl8tC42u4wMUvxzEL68T_wheBanJoI6bThk1VBUgtaGxlWzQvUUbWlExgv1LwcpBT3uJcLNAi8cqpObNlbCvo_zZ_6D8OdwJo-tTXeM-7G26rXuBDs5GH8DNpn3fTvHaTuaLo4O4t_FuOV80X_8A9Nn-og |
| linkProvider | Directory of Open Access Journals |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3NbtNAEF5VrVDhgPgVhgJ7AAEHq2t71xsjVSiBRAltQ1S1Um_Len_CISTBdqh660Nw4WV4mD4Js2u7rUCCU69RtLZ2dr-ZbzwzH0IvDNNW8liGNiGdkGpL4UoxuHg6IobnlnIv97Y_TodH9OMxO15Dv9peGFdW2WKiB2q9UC5Hvh07XXjippO9W34LnWqU-7raSmjIRlpB7_gRY01jx645PQEKV-6MPoC9X8bxoH_4fhg2KgOhStKsChmRkbJM55RzQ5QF8FLg5MFNRppKDu5RQYjuB30BNQESl0ex-xylaKpZxzjVCHABGzShGZC_jV5_PDm4zPJwlgFPq2cKwQJke1XXWxgAGUKdRPIVd-hVA_72DbfQ5mq-lKcncja74vwGd9DtJmrF3fqY3UVrZn4P3fDVo6q8j74f-B51V0GNh9Jlq8_PfpZ4pCEKxQNX_oUnBbDzqT8G2OV-cSN8jyemAK-X14nD87Mf0Vvck7As7s6msP_Vl68lhsAaf_IVs_4R_brkvXyAjq5lqx-i9flibh4hnKcs0VFkk5wCRSREcsnyVEpjATANTwP0ut1XsazndgjgO84E4g8TBKjn9v3ib27gtv9hUUxFc38FAB3lWR5pZSxlNpZuhIDMLE2AojBOA_TKWU04WKgKqWTT3QBv6wZsiS6E2YDlHcIDtNUaVjR4UYrL0x2gNxfG_t-bP_73Us_R5vBwf0_sjca7T9DNGMKzuotyC61Xxco8hXCqyp81Zxajz9d9TX4DYwAzNA |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3NbtNAEF5VrYByQPwKQ4E9gICDlbW9602QKpTQRAmFEBUq9eauvbvpISTBdqh660Nw4ZV4jD4JM2u7rUCCU6-WtbZ2dr752Zn5CHluhLZKhsq3EWv7XFsOKiVA8XTAjEwtl47u7eM4Hu7z9wfiYI38anphsKyywUQH1HqRYY68FSIvPMPpZC1bl0VMdgZvl998ZJDCm9aGTkPVNAt6240bq5s8ds3JMYRzxfZoB2T_IgwH_S_vhn7NOOBnUdwpfcFUkFmhUy6lYZkFIMvA4IPJDDRXEkxlBu66G_oFYQoEdGkQ4tVUxmMt2gYZJMAcbODlF4DERq8_nuxdZHyk6EDMVs0XggVYa1XVXhgAHMaRLvmSaXQMAn_biZvkxmq-VCfHaja7ZAgHt8mt2oOl3erI3SFrZn6XXHOVpFlxj3zfc_3qWE1Nhwoz12enPws60uCR0gGWgtFJDpH61B0Jinlg-nlpMHNPJyYHC5hWScSz0x_BG9pTsCztzqaw_-XR14KCk00_uepZ94l-Vf5e3Cf7V7LVD8j6fDE3DwlNYxHpILBRyiFcZExJJdJYKWMBPI2MPfKq2ddkWc3wSCD2QREkf4jAIz3c9_PXcPi2e7DIp0mtywmAHpedNNCZsVzYUOE4AdWxPIJwRUjukZcotQQhosxVpupOB_hbHLaVdMHlBlxvM-mRrUawSY0dRXJx0j3y-lzY__vzR_9e6hm5DuqSfBiNdx-TzRA8taqhcousl_nKPAHPqkyf1keWksOr1pLfed43Yw |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NbxMxELUgFQIOfCMCBfmABBy2a-_a64QLSlGjgESJEJHKyfJnhAhJtLspglN_BBf-Xn8JY69TVeWA4Bo5iZPxzLw3-zyD0FPHrVeiUJkvySBj1jNwKQ6OZylxQnsm4ri3d4fVZMbeHvGjVHBrkqwSqPjnGKQLyD9RCZEPc0pzJki-tv7Vcaok0QoIMyvBRS6jnYoDFu-hndnhdPQpTJTbvrfr51MCt883ndbBgYMTFsYTn0tFsWP_n3H5Orq6Wa7V929qsTiXeMY3kdxuudObfNnbtHrP_LjQzfH_f9MtdCNhUjzqDtFtdMkt76ArURtqmrvo-EO8gR700XiiQi369ORXg99YwJh4HMRdeFoD955HI-NQ2cVprD2euhpymu7KgqcnP-lLvK_gY_FoMV_VsPJrgwE24_dRDxu_4qATtDf30Gx88PH1JEvjGjJTVsM240RR47nVTAhHjIcsYAAtAd6glikB_7kBrhM7pgHHAzasaRGe6xlWWT5wvLyPesvV0j1AWFe8tJT6UjMggIQoobiulHIewqETVR8931pOrruuHBLYTDCyvGDkPtoPlj1bFtppxxdW9Vwm75QQxpgYamqN84z7QoUGAWroWQkEhAvWR8_CuZDB6dtaGZXuLsBuQ_ssOQIQDSYbENFHu9ujI1M0aCSQ2hLiKhvAbl6cHae_7fzhP6x9hK4VgL66S5K7qNfWG_cY0FKrnySX-A1zHBIS |
| 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=Revisiting+Hansen%E2%80%99s+Ideal+Frame+Propagation+with+Special+Perturbations%E2%80%941%3A+Basic+Algorithms+for+Osculating+Elements&rft.jtitle=Universe+%28Basel%29&rft.au=Martin+Lara&rft.au=Hodei+Urrutxua&rft.date=2023-11-01&rft.pub=MDPI+AG&rft.eissn=2218-1997&rft.volume=9&rft.issue=11&rft.spage=470&rft_id=info:doi/10.3390%2Funiverse9110470&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_048479b1dcef45f2a4316a9f43882574 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2218-1997&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2218-1997&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2218-1997&client=summon |