Higher order approximation to the Hill problem dynamics about the libration points
•A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical solution captures all the relevant periodic orbits. An analytical solution to the Hill problem Hamiltonian expanded about the libration points has...
Gespeichert in:
| Veröffentlicht in: | Communications in nonlinear science & numerical simulation Jg. 59; S. 612 - 628 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
01.06.2018
Elsevier Science Ltd |
| Schlagworte: | |
| ISSN: | 1007-5704, 1878-7274 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | •A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical solution captures all the relevant periodic orbits.
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt–Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits. |
|---|---|
| AbstractList | An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt–Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits. •A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical solution captures all the relevant periodic orbits. An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt–Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits. |
| Author | Pérez, Iván L. López, Rosario Lara, Martin |
| Author_xml | – sequence: 1 givenname: Martin surname: Lara fullname: Lara, Martin email: mlara0@gmail.com organization: ETSI Aeronáuticos, Plaza del Cardenal Cisneros 3, Madrid 28040, Spain – sequence: 2 givenname: Iván L. surname: Pérez fullname: Pérez, Iván L. email: ivan.perez@unirioja.es organization: Scientific Computing Group (GRUCACI), University of La Rioja, San José de Calasanz 31, 26004 Logroño, Spain – sequence: 3 givenname: Rosario surname: López fullname: López, Rosario email: rlgomez@riojasalud.es organization: Scientific Computing Group (GRUCACI), Center for Biomedical Research of La Rioja, Piqueras 98, 26006 Logroño, Spain |
| BookMark | eNqFkMFPwyAUxomZiXP6F3hp4rkVKIX14MEs6kyWmBg9kxZeHU0HE5hx_71s9eRBLzzyvfd78H3naGKdBYSuCC4IJvymL5QNNhQUE1EQWmAsTtCUzMU8F1SwSbonKa8EZmfoPIQeJ6qu2BS9LM37GnzmvE5ns91692U2TTTOZtFlcQ3Z0gxDlvR2gE2m97bZGBWypnW7eOwPpvUjsHXGxnCBTrtmCHD5U2fo7eH-dbHMV8-PT4u7Va7KksS8Bq40ZryqMOaccMrahrVUlLTF9bwD0EJVwISgXYdryjUHzrhiTJNKgCblDF2Pe9PfPnYQouzdztv0pKSYUVpSMsdpqhynlHcheOjk1ieDfi8JlofwZC-P4clDeJJQmZJKVP2LUiYeTUbfmOEf9nZkIZn_NOBlUAasAm08qCi1M3_y35P7jjk |
| CitedBy_id | crossref_primary_10_1007_s10569_022_10076_6 crossref_primary_10_1007_s11071_024_09757_8 crossref_primary_10_1016_j_actaastro_2022_01_022 crossref_primary_10_1007_s10509_022_04135_5 crossref_primary_10_1007_s11071_023_08325_w crossref_primary_10_1007_s10509_019_3497_0 crossref_primary_10_1007_s10509_021_03926_6 crossref_primary_10_2514_1_G006519 crossref_primary_10_1007_s11071_018_4304_0 crossref_primary_10_1007_s11071_025_10926_6 crossref_primary_10_1016_j_cnsns_2019_105053 crossref_primary_10_2478_AMNS_2018_2_00042 crossref_primary_10_1155_2021_9963761 crossref_primary_10_1007_s11071_024_10347_x |
| Cites_doi | 10.1007/BF00696185 10.1007/BF01229007 10.1007/BF01229511 10.1007/BF01229494 10.1007/BF01218480 10.1007/BF00641660 10.2514/1.5686 10.1080/14689360412331313039 10.1098/rspa.1982.0106 10.2307/2369430 10.1007/s10569-010-9286-2 10.1007/BF01231143 10.1016/S0167-2789(99)00211-0 10.1016/S0167-2789(01)00312-8 10.1007/BF01238756 10.1080/10586458.1999.10504397 10.1007/s00332-015-9232-2 10.1007/BF01230405 10.1016/j.cnsns.2008.09.016 10.1016/j.cnsns.2014.01.019 10.1007/BF01227656 10.1016/S0094-5765(98)00177-5 10.1016/j.cnsns.2015.08.004 10.1016/S0167-2789(99)00042-1 10.1016/0019-1035(65)90002-3 10.1007/BF01230629 10.2514/1.22372 10.1007/BF01227511 10.1007/BF01609411 10.1016/0019-1035(86)90089-8 10.1023/A:1022518422926 10.1007/s10569-017-9778-4 10.1007/BF01358403 10.2514/1.53097 10.1007/s11012-007-9060-z 10.1007/BF01457962 10.1080/14689360412331304291 10.1007/BF00051691 10.1007/BF01232832 |
| ContentType | Journal Article |
| Copyright | 2017 Elsevier B.V. Copyright Elsevier Science Ltd. Jun 2018 |
| Copyright_xml | – notice: 2017 Elsevier B.V. – notice: Copyright Elsevier Science Ltd. Jun 2018 |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cnsns.2017.12.007 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 1878-7274 |
| EndPage | 628 |
| ExternalDocumentID | 10_1016_j_cnsns_2017_12_007 S100757041730429X |
| GroupedDBID | --K --M -01 -0A -0I -0Y -SA -S~ .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VR 5VS 7-5 71M 8P~ 92M 9D9 9DA AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABFNM ABJNI ABMAC ABNEU ABXDB ABYKQ ACAZW ACDAQ ACFVG ACGFS ACNNM ACRLP ADBBV ADEZE ADGUI ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AFUIB AGHFR AGUBO AGYEJ AHJVU AIEXJ AIGVJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CAJEA CAJUS CCEZO CCVFK CHBEP CS3 CUBFJ DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FA0 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HVGLF HZ~ IHE J1W JJJVA JUIAU KOM M41 MHUIS MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q-- Q-0 Q38 R-A R-I R2- RIG ROL RPZ RT1 RT9 S.. SDF SDG SES SEW SPC SPCBC SPD SSQ SST SSW SSZ T5K T8Q T8Y U1F U1G U5A U5I U5K UHS ~G- ~LA 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS SSH |
| ID | FETCH-LOGICAL-c331t-9e6cd0465500661624ba4b2732b098feed7c5e4772ff0926d6e646c44d157ed13 |
| ISICitedReferencesCount | 13 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000425327800046&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1007-5704 |
| IngestDate | Fri Jul 25 05:47:24 EDT 2025 Tue Nov 18 22:08:41 EST 2025 Sat Nov 29 02:22:52 EST 2025 Fri Feb 23 02:25:46 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Perturbation theory Hill’s problem Periodic orbits Libration points Complex variables Floating point arithmetic Hopf variables |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c331t-9e6cd0465500661624ba4b2732b098feed7c5e4772ff0926d6e646c44d157ed13 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2042232180 |
| PQPubID | 2047477 |
| PageCount | 17 |
| ParticipantIDs | proquest_journals_2042232180 crossref_primary_10_1016_j_cnsns_2017_12_007 crossref_citationtrail_10_1016_j_cnsns_2017_12_007 elsevier_sciencedirect_doi_10_1016_j_cnsns_2017_12_007 |
| PublicationCentury | 2000 |
| PublicationDate | June 2018 2018-06-00 20180601 |
| PublicationDateYYYYMMDD | 2018-06-01 |
| PublicationDate_xml | – month: 06 year: 2018 text: June 2018 |
| PublicationDecade | 2010 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Communications in nonlinear science & numerical simulation |
| PublicationYear | 2018 |
| Publisher | Elsevier B.V Elsevier Science Ltd |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier Science Ltd |
| References | Alessi, Gómez, Masdemont (bib0005) 2009; 14 Henrard (bib0047) 1970; 1 Lara, San-Juan (bib0044) 2005; 28 Jorba (bib0050) 1999; 8 San-Juan (bib0049) 1994 Giorgilli, Galgani (bib0039) 1978; 17 Celletti, Pucacco, Stella (bib0038) 2015; 25 Lara, Russell, Villac (bib0013) 2007; 30 Deprit (bib0037) 1991; 51 Kummer (bib0034) 1976; 48 Hénon (bib0026) 1969; 1 Gómez, Marcote, Mondelo (bib0032) 2005; 20 Simó, Stuchi (bib0031) 2000; 140 Hénon (bib0009) 1965; 28 Vashkov’yak (bib0022) 1999; 25 Celletti, Chierchia (bib0051) 1988; 118 Petit, Hénon (bib0021) 1986; 66 Cushman (bib0035) 1982; 382 Deprit, Delie (bib0045) 1965; 4 Henrard (bib0048) 1988; 45 Zagouras, Markellos (bib0030) 1985; 35 Boccaletti, Pucacco (bib0041) 2002 Deprit, Deprit (bib0043) 1989 Koon, Lo, Marsden, Ross (bib0004) 2001 Szebehely (bib0001) 1967 Lara, Palacián, Russell (bib0024) 2010; 108 Howell (bib0012) 1984; 32 Hénon (bib0028) 2003; 85 Breakwell, Brown (bib0011) 1979; 20 Gómez, Jorba, Masdemont, Simó (bib0046) 1991 Gómez, Lo, Masdemont (bib0006) 2003 Gómez, Jorba, Masdemont, Simó (bib0002) 1993; 56 Michalodimitrakis (bib0029) 1980; 68 Farquhar, Kamel (bib0016) 1973; 7 Lara, Russell, Villac (bib0023) 2007; 42 Masdemont (bib0019) 2005; 20 Topputo (bib0008) 2016; 32 Deprit (bib0040) 1969; 1 Lara (bib0033) 2017; 129 Gómez, Jorba, Masdemont, Simó (bib0003) 1998; 43 Richardson (bib0017) 1980; 22 Hopf (bib0036) 1931; 104 Gómez, Mondelo (bib0015) 2001; 157 Lei, Xu (bib0007) 2014; 19 Howell, Pernicka (bib0014) 1988; 41 Hill (bib0020) 1878; 1 Peláez, Lara, Bombardelli, Lucas, Sanjurjo-Rivo, Curreli (bib0025) 2012; 35 Hénon (bib0010) 1965; 28 Deprit, Rom (bib0042) 1970; 2 Jorba, Masdemont (bib0018) 1999; 132 Hénon (bib0027) 1974; 30 Lara (10.1016/j.cnsns.2017.12.007_bib0044) 2005; 28 Alessi (10.1016/j.cnsns.2017.12.007_bib0005) 2009; 14 Zagouras (10.1016/j.cnsns.2017.12.007_bib0030) 1985; 35 Deprit (10.1016/j.cnsns.2017.12.007_sbref0042) 1989 Peláez (10.1016/j.cnsns.2017.12.007_bib0025) 2012; 35 Gómez (10.1016/j.cnsns.2017.12.007_bib0015) 2001; 157 Deprit (10.1016/j.cnsns.2017.12.007_bib0040) 1969; 1 Simó (10.1016/j.cnsns.2017.12.007_bib0031) 2000; 140 Jorba (10.1016/j.cnsns.2017.12.007_bib0018) 1999; 132 Hill (10.1016/j.cnsns.2017.12.007_bib0020) 1878; 1 Howell (10.1016/j.cnsns.2017.12.007_bib0014) 1988; 41 Lara (10.1016/j.cnsns.2017.12.007_bib0023) 2007; 42 Farquhar (10.1016/j.cnsns.2017.12.007_bib0016) 1973; 7 Kummer (10.1016/j.cnsns.2017.12.007_bib0034) 1976; 48 Celletti (10.1016/j.cnsns.2017.12.007_bib0038) 2015; 25 Boccaletti (10.1016/j.cnsns.2017.12.007_bib0041) 2002 Lara (10.1016/j.cnsns.2017.12.007_bib0013) 2007; 30 Giorgilli (10.1016/j.cnsns.2017.12.007_bib0039) 1978; 17 Gómez (10.1016/j.cnsns.2017.12.007_bib0046) 1991 Celletti (10.1016/j.cnsns.2017.12.007_bib0051) 1988; 118 Topputo (10.1016/j.cnsns.2017.12.007_bib0008) 2016; 32 Jorba (10.1016/j.cnsns.2017.12.007_sbref0049) 1999; 8 Vashkov’yak (10.1016/j.cnsns.2017.12.007_bib0022) 1999; 25 Lara (10.1016/j.cnsns.2017.12.007_bib0033) 2017; 129 Michalodimitrakis (10.1016/j.cnsns.2017.12.007_bib0029) 1980; 68 Lara (10.1016/j.cnsns.2017.12.007_bib0024) 2010; 108 Henrard (10.1016/j.cnsns.2017.12.007_bib0047) 1970; 1 Henrard (10.1016/j.cnsns.2017.12.007_bib0048) 1988; 45 Richardson (10.1016/j.cnsns.2017.12.007_bib0017) 1980; 22 Deprit (10.1016/j.cnsns.2017.12.007_bib0037) 1991; 51 Masdemont (10.1016/j.cnsns.2017.12.007_bib0019) 2005; 20 Breakwell (10.1016/j.cnsns.2017.12.007_bib0011) 1979; 20 Petit (10.1016/j.cnsns.2017.12.007_bib0021) 1986; 66 Deprit (10.1016/j.cnsns.2017.12.007_bib0042) 1970; 2 Gómez (10.1016/j.cnsns.2017.12.007_bib0002) 1993; 56 Szebehely (10.1016/j.cnsns.2017.12.007_sbref0001) 1967 Lei (10.1016/j.cnsns.2017.12.007_bib0007) 2014; 19 Gómez (10.1016/j.cnsns.2017.12.007_bib0003) 1998; 43 Hénon (10.1016/j.cnsns.2017.12.007_bib0009) 1965; 28 Hénon (10.1016/j.cnsns.2017.12.007_bib0028) 2003; 85 San-Juan (10.1016/j.cnsns.2017.12.007_bib0049) 1994 Hénon (10.1016/j.cnsns.2017.12.007_bib0010) 1965; 28 Hénon (10.1016/j.cnsns.2017.12.007_bib0026) 1969; 1 Hénon (10.1016/j.cnsns.2017.12.007_bib0027) 1974; 30 Gómez (10.1016/j.cnsns.2017.12.007_bib0032) 2005; 20 Koon (10.1016/j.cnsns.2017.12.007_bib0004) 2001 Hopf (10.1016/j.cnsns.2017.12.007_bib0036) 1931; 104 Deprit (10.1016/j.cnsns.2017.12.007_bib0045) 1965; 4 Howell (10.1016/j.cnsns.2017.12.007_bib0012) 1984; 32 Gómez (10.1016/j.cnsns.2017.12.007_sbref0006) 2003 Cushman (10.1016/j.cnsns.2017.12.007_bib0035) 1982; 382 |
| References_xml | – volume: 42 start-page: 511 year: 2007 end-page: 515 ident: bib0023 article-title: Fast estimation of stable regions in real models publication-title: Meccanica – volume: 132 start-page: 189 year: 1999 end-page: 213 ident: bib0018 article-title: Dynamics in the center manifold of the collinear points of the restricted three body problem publication-title: Physica D Nonlinear Phenomena – year: 1991 ident: bib0046 article-title: Study refinement of semi-analytical halo orbit theory publication-title: Technical report contract 8625/89/D/MD(SC), European space operations center, Robert-Bosch-Strasse 5, 64293 Darmstadt, Germany – volume: 35 start-page: 257 year: 1985 end-page: 267 ident: bib0030 article-title: Three-dimensional periodic solutions around equilibrium points in Hill’s problem publication-title: Celestial Mech – volume: 129 start-page: 285 year: 2017 end-page: 306 ident: bib0033 article-title: A hopf variables view on the libration points dynamics publication-title: Celestial Mech Dyn Astron – volume: 28 start-page: 291 year: 2005 end-page: 297 ident: bib0044 article-title: Dynamic behavior of an orbiter around europa publication-title: J Guidance Control Dyn – volume: 66 start-page: 536 year: 1986 end-page: 555 ident: bib0021 article-title: Satellite encounters publication-title: Icarus – volume: 28 start-page: 499 year: 1965 ident: bib0009 article-title: Exploration numérique du problème restreint. i. masseségales ; orbites périodiques publication-title: Annales d’Astrophysique – year: 1967 ident: bib0001 article-title: Theory of orbits. the restricted problem of three bodies – volume: 25 start-page: 343 year: 2015 end-page: 370 ident: bib0038 article-title: Lissajous and halo orbits in the restricted three-body problem publication-title: J NonLinear Sci – volume: 85 start-page: 223 year: 2003 end-page: 246 ident: bib0028 article-title: New families of periodic orbits in Hill’s problem of three bodies publication-title: Celestial Mech Dyn Astron – volume: 30 start-page: 317 year: 1974 ident: bib0027 article-title: Vertical stability of periodic orbits in the restricted problem. II. Hill’s case publication-title: Astron Astrophys – volume: 108 start-page: 1 year: 2010 end-page: 22 ident: bib0024 article-title: Mission design through averaging of perturbed Keplerian systems: the paradigm of an enceladus orbiter publication-title: Celestial Mech Dyn Astron – volume: 8 start-page: 155 year: 1999 end-page: 195 ident: bib0050 article-title: A methodology for the numerical computation of normal forms, centre manifolds and first integrals of hamiltonian systems publication-title: Exp Math – volume: 41 start-page: 107 year: 1988 end-page: 124 ident: bib0014 article-title: Numerical determination of lissajous trajectories in the restricted three-body problem publication-title: Celestial Mech – volume: 56 start-page: 541 year: 1993 end-page: 562 ident: bib0002 article-title: Study of the transfer from the earth to a halo orbit around the equilibrium point l1 publication-title: Celestial Mech Dyn Astron – volume: 20 start-page: 59 year: 2005 end-page: 113 ident: bib0019 article-title: High-order expansions of invariant manifolds of libration point orbits with applications to mission design publication-title: Dyn Syst – volume: 43 start-page: 493 year: 1998 end-page: 520 ident: bib0003 article-title: Study of the transfer between halo orbits publication-title: Acta Astronaut – volume: 382 start-page: 361 year: 1982 end-page: 371 ident: bib0035 article-title: Geometry of the bifurcations of the normalized reduced Henon–Heiles family publication-title: Proc R Soc Lond Series A – volume: 30 start-page: 409 year: 2007 end-page: 418 ident: bib0013 article-title: Classification of the distant stability regions at europa publication-title: J Guidance Control Dyn – volume: 48 start-page: 53 year: 1976 end-page: 79 ident: bib0034 article-title: On resonant non linearly coupled oscillators with two equal frequencies publication-title: Commun Math Phys – start-page: 308 year: 1989 end-page: 316 ident: bib0043 article-title: Massively parallel symbolic computation publication-title: Proceedings of the ACM-SIGSAM 1989 international symposium on symbolic and algebraic computation, ISSAC ’89 – start-page: 2327 year: 2001 end-page: 2343 ident: bib0004 article-title: The genesis trajectory and heteroclinic connections publication-title: AAS/aiaa astrodynamics conference 1999, vol. 103 of advances in the astronautical sciences – volume: 25 start-page: 476 year: 1999 end-page: 481 ident: bib0022 article-title: Evolution of the orbits of distant satellites of uranus publication-title: Astron Lett – volume: 35 start-page: 222 year: 2012 end-page: 233 ident: bib0025 article-title: Periodic orbits of a Hill-tether problem originated from collinear points publication-title: J Guidance Control Dyn – year: 1994 ident: bib0049 article-title: ATESAT: Automatization of theories and ephemeris in the artificial satellite problem publication-title: Technical report CT/TI/MS/MN/94-250, centre national d’études spatiales, 18, avenue Edouard Belin - 31401 Toulouse Cedex 9, France – volume: 4 start-page: 242 year: 1965 end-page: 266 ident: bib0045 article-title: Trojan orbits. i. d’alembert series at l publication-title: Icarus – year: 2003 ident: bib0006 article-title: Libration point orbits and applications publication-title: World scientfic – volume: 28 start-page: 992 year: 1965 ident: bib0010 article-title: Exploration numérique du problème restreint. II. masses égales, stabilité des orbites périodiques publication-title: Annales d’Astrophysique – volume: 20 start-page: 389 year: 1979 end-page: 404 ident: bib0011 article-title: The ’halo’ family of 3-dimensional periodic orbits in the earth-moon restricted 3-body problem publication-title: Celestial Mech – volume: 19 start-page: 3374 year: 2014 end-page: 3398 ident: bib0007 article-title: High-order solutions around triangular libration points in the elliptic restricted three-body problem and applications to low energy transfers publication-title: Commun Nonlinear Sci Numer Simul – volume: 32 start-page: 53 year: 1984 ident: bib0012 article-title: Three-dimensional periodic halo orbits publication-title: Celestial Mech – volume: 104 start-page: 637 year: 1931 end-page: 665 ident: bib0036 article-title: Über die abbildungen der dreidimensionalen sphäre auf die kugelfläche publication-title: Mathematische Annalen – volume: 7 start-page: 458 year: 1973 end-page: 473 ident: bib0016 article-title: Quasi-periodic orbits about the translunar libration point publication-title: Celestial Mech – volume: 68 start-page: 253 year: 1980 end-page: 268 ident: bib0029 article-title: Hill’S problem - families of three-dimensional periodic orbits. i publication-title: Astrophys Space Sci – volume: 140 start-page: 1 year: 2000 end-page: 32 ident: bib0031 article-title: Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem publication-title: Physica D Nonlinear Phenomena – volume: 20 start-page: 115 year: 2005 end-page: 147 ident: bib0032 article-title: The invariant manifold structure of the spatial Hill’s problem publication-title: Dyn Syst – volume: 1 start-page: 5 year: 1878 end-page: 26 ident: bib0020 article-title: Researches in the lunar theory publication-title: Am J Math – volume: 1 start-page: 437 year: 1970 end-page: 466 ident: bib0047 article-title: Periodic orbits emanating from a resonant equilibrium publication-title: Celestial Mech – volume: 118 start-page: 119 year: 1988 end-page: 161 ident: bib0051 article-title: Construction of analytic KAM surfaces and effective stability bounds publication-title: Commun Math Phys – volume: 2 start-page: 166 year: 1970 end-page: 206 ident: bib0042 article-title: The main problem of artificial satellite theory for small and moderate eccentricities publication-title: Celestial Mech – volume: 157 start-page: 283 year: 2001 end-page: 321 ident: bib0015 article-title: The dynamics around the collinear equilibrium points of the {RTBP} publication-title: Physica D – volume: 32 start-page: 89 year: 2016 end-page: 98 ident: bib0008 article-title: Fast numerical approximation of invariant manifolds in the circular restricted three-body problem publication-title: Commun Nonlinear Sci Numer Simul – year: 2002 ident: bib0041 article-title: Theory of orbits. volume 2: perturbative and geometrical methods publication-title: 1st Edition, astronomy and astrophysics library – volume: 1 start-page: 12 year: 1969 end-page: 30 ident: bib0040 article-title: Canonical transformations depending on a small parameter publication-title: Celestial Mech – volume: 22 start-page: 241 year: 1980 end-page: 253 ident: bib0017 article-title: Analytic construction of periodic orbits about the collinear points publication-title: Celestial Mech – volume: 14 start-page: 4153 year: 2009 end-page: 4167 ident: bib0005 article-title: Leaving the moon by means of invariant manifolds of libration point orbits publication-title: Commun Nonlinear Sci Numer Simul – volume: 51 start-page: 201 year: 1991 end-page: 225 ident: bib0037 article-title: The lissajous transformation. i - basics publication-title: Celestial Mech Dyn Astron – volume: 17 start-page: 267 year: 1978 end-page: 280 ident: bib0039 article-title: Formal integrals for an autonomous Hamiltonian system near an equilibrium point publication-title: Celestial Mech – volume: 1 start-page: 223 year: 1969 end-page: 238 ident: bib0026 article-title: Numerical exploration of the restricted problem, v. hill’s case: periodic orbits and their stability publication-title: Astron Astrophys – volume: 45 start-page: 245 year: 1988 end-page: 253 ident: bib0048 article-title: A survey of poisson series processors publication-title: Celestial Mech – volume: 56 start-page: 541 year: 1993 ident: 10.1016/j.cnsns.2017.12.007_bib0002 article-title: Study of the transfer from the earth to a halo orbit around the equilibrium point l1 publication-title: Celestial Mech Dyn Astron doi: 10.1007/BF00696185 – volume: 45 start-page: 245 year: 1988 ident: 10.1016/j.cnsns.2017.12.007_bib0048 article-title: A survey of poisson series processors publication-title: Celestial Mech doi: 10.1007/BF01229007 – volume: 22 start-page: 241 year: 1980 ident: 10.1016/j.cnsns.2017.12.007_bib0017 article-title: Analytic construction of periodic orbits about the collinear points publication-title: Celestial Mech doi: 10.1007/BF01229511 – volume: 2 start-page: 166 issue: 2 year: 1970 ident: 10.1016/j.cnsns.2017.12.007_bib0042 article-title: The main problem of artificial satellite theory for small and moderate eccentricities publication-title: Celestial Mech doi: 10.1007/BF01229494 – volume: 118 start-page: 119 year: 1988 ident: 10.1016/j.cnsns.2017.12.007_bib0051 article-title: Construction of analytic KAM surfaces and effective stability bounds publication-title: Commun Math Phys doi: 10.1007/BF01218480 – start-page: 308 year: 1989 ident: 10.1016/j.cnsns.2017.12.007_sbref0042 article-title: Massively parallel symbolic computation – year: 1967 ident: 10.1016/j.cnsns.2017.12.007_sbref0001 – volume: 68 start-page: 253 year: 1980 ident: 10.1016/j.cnsns.2017.12.007_bib0029 article-title: Hill’S problem - families of three-dimensional periodic orbits. i publication-title: Astrophys Space Sci doi: 10.1007/BF00641660 – volume: 28 start-page: 499 year: 1965 ident: 10.1016/j.cnsns.2017.12.007_bib0009 article-title: Exploration numérique du problème restreint. i. masseségales ; orbites périodiques publication-title: Annales d’Astrophysique – volume: 28 start-page: 291 issue: 2 year: 2005 ident: 10.1016/j.cnsns.2017.12.007_bib0044 article-title: Dynamic behavior of an orbiter around europa publication-title: J Guidance Control Dyn doi: 10.2514/1.5686 – volume: 20 start-page: 115 issue: 1 year: 2005 ident: 10.1016/j.cnsns.2017.12.007_bib0032 article-title: The invariant manifold structure of the spatial Hill’s problem publication-title: Dyn Syst doi: 10.1080/14689360412331313039 – volume: 382 start-page: 361 year: 1982 ident: 10.1016/j.cnsns.2017.12.007_bib0035 article-title: Geometry of the bifurcations of the normalized reduced Henon–Heiles family publication-title: Proc R Soc Lond Series A doi: 10.1098/rspa.1982.0106 – volume: 1 start-page: 5 year: 1878 ident: 10.1016/j.cnsns.2017.12.007_bib0020 article-title: Researches in the lunar theory publication-title: Am J Math doi: 10.2307/2369430 – volume: 108 start-page: 1 issue: 1 year: 2010 ident: 10.1016/j.cnsns.2017.12.007_bib0024 article-title: Mission design through averaging of perturbed Keplerian systems: the paradigm of an enceladus orbiter publication-title: Celestial Mech Dyn Astron doi: 10.1007/s10569-010-9286-2 – volume: 1 start-page: 437 year: 1970 ident: 10.1016/j.cnsns.2017.12.007_bib0047 article-title: Periodic orbits emanating from a resonant equilibrium publication-title: Celestial Mech doi: 10.1007/BF01231143 – year: 2002 ident: 10.1016/j.cnsns.2017.12.007_bib0041 article-title: Theory of orbits. volume 2: perturbative and geometrical methods – year: 2003 ident: 10.1016/j.cnsns.2017.12.007_sbref0006 article-title: Libration point orbits and applications – volume: 140 start-page: 1 year: 2000 ident: 10.1016/j.cnsns.2017.12.007_bib0031 article-title: Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem publication-title: Physica D Nonlinear Phenomena doi: 10.1016/S0167-2789(99)00211-0 – volume: 1 start-page: 223 year: 1969 ident: 10.1016/j.cnsns.2017.12.007_bib0026 article-title: Numerical exploration of the restricted problem, v. hill’s case: periodic orbits and their stability publication-title: Astron Astrophys – volume: 30 start-page: 317 year: 1974 ident: 10.1016/j.cnsns.2017.12.007_bib0027 article-title: Vertical stability of periodic orbits in the restricted problem. II. Hill’s case publication-title: Astron Astrophys – year: 1994 ident: 10.1016/j.cnsns.2017.12.007_bib0049 article-title: ATESAT: Automatization of theories and ephemeris in the artificial satellite problem – volume: 157 start-page: 283 issue: 4 year: 2001 ident: 10.1016/j.cnsns.2017.12.007_bib0015 article-title: The dynamics around the collinear equilibrium points of the {RTBP} publication-title: Physica D doi: 10.1016/S0167-2789(01)00312-8 – volume: 41 start-page: 107 year: 1988 ident: 10.1016/j.cnsns.2017.12.007_bib0014 article-title: Numerical determination of lissajous trajectories in the restricted three-body problem publication-title: Celestial Mech doi: 10.1007/BF01238756 – volume: 8 start-page: 155 issue: 2 year: 1999 ident: 10.1016/j.cnsns.2017.12.007_sbref0049 article-title: A methodology for the numerical computation of normal forms, centre manifolds and first integrals of hamiltonian systems publication-title: Exp Math doi: 10.1080/10586458.1999.10504397 – volume: 25 start-page: 343 year: 2015 ident: 10.1016/j.cnsns.2017.12.007_bib0038 article-title: Lissajous and halo orbits in the restricted three-body problem publication-title: J NonLinear Sci doi: 10.1007/s00332-015-9232-2 – volume: 20 start-page: 389 year: 1979 ident: 10.1016/j.cnsns.2017.12.007_bib0011 article-title: The ’halo’ family of 3-dimensional periodic orbits in the earth-moon restricted 3-body problem publication-title: Celestial Mech doi: 10.1007/BF01230405 – volume: 14 start-page: 4153 issue: 12 year: 2009 ident: 10.1016/j.cnsns.2017.12.007_bib0005 article-title: Leaving the moon by means of invariant manifolds of libration point orbits publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2008.09.016 – volume: 19 start-page: 3374 issue: 9 year: 2014 ident: 10.1016/j.cnsns.2017.12.007_bib0007 article-title: High-order solutions around triangular libration points in the elliptic restricted three-body problem and applications to low energy transfers publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2014.01.019 – volume: 35 start-page: 257 year: 1985 ident: 10.1016/j.cnsns.2017.12.007_bib0030 article-title: Three-dimensional periodic solutions around equilibrium points in Hill’s problem publication-title: Celestial Mech doi: 10.1007/BF01227656 – volume: 43 start-page: 493 issue: 9 year: 1998 ident: 10.1016/j.cnsns.2017.12.007_bib0003 article-title: Study of the transfer between halo orbits publication-title: Acta Astronaut doi: 10.1016/S0094-5765(98)00177-5 – volume: 32 start-page: 89 year: 2016 ident: 10.1016/j.cnsns.2017.12.007_bib0008 article-title: Fast numerical approximation of invariant manifolds in the circular restricted three-body problem publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2015.08.004 – volume: 132 start-page: 189 year: 1999 ident: 10.1016/j.cnsns.2017.12.007_bib0018 article-title: Dynamics in the center manifold of the collinear points of the restricted three body problem publication-title: Physica D Nonlinear Phenomena doi: 10.1016/S0167-2789(99)00042-1 – volume: 4 start-page: 242 year: 1965 ident: 10.1016/j.cnsns.2017.12.007_bib0045 article-title: Trojan orbits. i. d’alembert series at l4 publication-title: Icarus doi: 10.1016/0019-1035(65)90002-3 – volume: 1 start-page: 12 issue: 1 year: 1969 ident: 10.1016/j.cnsns.2017.12.007_bib0040 article-title: Canonical transformations depending on a small parameter publication-title: Celestial Mech doi: 10.1007/BF01230629 – volume: 30 start-page: 409 year: 2007 ident: 10.1016/j.cnsns.2017.12.007_bib0013 article-title: Classification of the distant stability regions at europa publication-title: J Guidance Control Dyn doi: 10.2514/1.22372 – volume: 7 start-page: 458 year: 1973 ident: 10.1016/j.cnsns.2017.12.007_bib0016 article-title: Quasi-periodic orbits about the translunar libration point publication-title: Celestial Mech doi: 10.1007/BF01227511 – start-page: 2327 year: 2001 ident: 10.1016/j.cnsns.2017.12.007_bib0004 article-title: The genesis trajectory and heteroclinic connections – volume: 25 start-page: 476 year: 1999 ident: 10.1016/j.cnsns.2017.12.007_bib0022 article-title: Evolution of the orbits of distant satellites of uranus publication-title: Astron Lett – volume: 48 start-page: 53 year: 1976 ident: 10.1016/j.cnsns.2017.12.007_bib0034 article-title: On resonant non linearly coupled oscillators with two equal frequencies publication-title: Commun Math Phys doi: 10.1007/BF01609411 – volume: 66 start-page: 536 year: 1986 ident: 10.1016/j.cnsns.2017.12.007_bib0021 article-title: Satellite encounters publication-title: Icarus doi: 10.1016/0019-1035(86)90089-8 – volume: 85 start-page: 223 year: 2003 ident: 10.1016/j.cnsns.2017.12.007_bib0028 article-title: New families of periodic orbits in Hill’s problem of three bodies publication-title: Celestial Mech Dyn Astron doi: 10.1023/A:1022518422926 – volume: 129 start-page: 285 issue: 3 year: 2017 ident: 10.1016/j.cnsns.2017.12.007_bib0033 article-title: A hopf variables view on the libration points dynamics publication-title: Celestial Mech Dyn Astron doi: 10.1007/s10569-017-9778-4 – volume: 32 start-page: 53 year: 1984 ident: 10.1016/j.cnsns.2017.12.007_bib0012 article-title: Three-dimensional periodic halo orbits publication-title: Celestial Mech doi: 10.1007/BF01358403 – volume: 35 start-page: 222 issue: 1 year: 2012 ident: 10.1016/j.cnsns.2017.12.007_bib0025 article-title: Periodic orbits of a Hill-tether problem originated from collinear points publication-title: J Guidance Control Dyn doi: 10.2514/1.53097 – volume: 42 start-page: 511 issue: 5 year: 2007 ident: 10.1016/j.cnsns.2017.12.007_bib0023 article-title: Fast estimation of stable regions in real models publication-title: Meccanica doi: 10.1007/s11012-007-9060-z – volume: 104 start-page: 637 year: 1931 ident: 10.1016/j.cnsns.2017.12.007_bib0036 article-title: Über die abbildungen der dreidimensionalen sphäre auf die kugelfläche publication-title: Mathematische Annalen doi: 10.1007/BF01457962 – volume: 28 start-page: 992 year: 1965 ident: 10.1016/j.cnsns.2017.12.007_bib0010 article-title: Exploration numérique du problème restreint. II. masses égales, stabilité des orbites périodiques publication-title: Annales d’Astrophysique – volume: 20 start-page: 59 issue: 1 year: 2005 ident: 10.1016/j.cnsns.2017.12.007_bib0019 article-title: High-order expansions of invariant manifolds of libration point orbits with applications to mission design publication-title: Dyn Syst doi: 10.1080/14689360412331304291 – volume: 51 start-page: 201 year: 1991 ident: 10.1016/j.cnsns.2017.12.007_bib0037 article-title: The lissajous transformation. i - basics publication-title: Celestial Mech Dyn Astron doi: 10.1007/BF00051691 – volume: 17 start-page: 267 year: 1978 ident: 10.1016/j.cnsns.2017.12.007_bib0039 article-title: Formal integrals for an autonomous Hamiltonian system near an equilibrium point publication-title: Celestial Mech doi: 10.1007/BF01232832 – year: 1991 ident: 10.1016/j.cnsns.2017.12.007_bib0046 article-title: Study refinement of semi-analytical halo orbit theory |
| SSID | ssj0016954 |
| Score | 2.3179333 |
| Snippet | •A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical... An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 612 |
| SubjectTerms | Approximation Complex variables Floating point arithmetic Hill’s problem Hopf variables Lagrangian equilibrium points Libration Libration points Nonlinear equations Orbits Periodic orbits Perturbation methods Perturbation theory Studies |
| Title | Higher order approximation to the Hill problem dynamics about the libration points |
| URI | https://dx.doi.org/10.1016/j.cnsns.2017.12.007 https://www.proquest.com/docview/2042232180 |
| Volume | 59 |
| WOSCitedRecordID | wos000425327800046&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1878-7274 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0016954 issn: 1007-5704 databaseCode: AIEXJ dateStart: 19960101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZWLQcuvBGFgnzgFlLl4TjxsaCiFlUVqgraW5S1HSlVyK4229X-E_4uY4_tvsSKHrhEu3ZsZXe-jGfG428I-ShbJYVKkriBxTxmsknjRplwWCNggJopbXNzfp6WZ2fVdCq-Tya__VmYdV8OQ7XZiMV_FTW0gbDN0dkHiDtMCg3wGYQOVxA7XP9J8C5zw3JqImX4psPzid7OPO76PnKVZCKFJelHl6Js-q0LbQcs5p2jegpsBjcPlNhc2gHJNppl5I8IGTQNV7gV1Edj98uVCAvJP40tbhQhhUFQzrhnv8SQ9snafk2H6PQgjDNNn_MF3nE-H8HPn98MW6TVdXqV07QmRlqUWHvYq2JHDo66lLv8alyWOZ4hv6fxMfhweSCHcTD062lpw7tYSvc2v_addS9kI_pEt8vaTlKbSeo0qy1LwW5WFgI0_u7hydH0W9ig4sIW2Au_whNa2dTBe8_yN6PnzvJvbZqLZ-SJc0boIYLoOZno4QV56hwT6tT--JKcI6aoxRS9hSm6mlPADDWYog5T1GOKWkzZ_oApiph6RX58Pbr4chy7YhyxzPN0FQvNpUoM256xUlOesVnDZmD8ZrNEVC2YWqUsNANnrW0TkXHFNWdcMqbSotQqzV-THQCkfkMoGPlCVoXKWZmzRIkKzHAJS41mLXjPidwjmf-3aumY6k3BlL7eIqk98ikMWiBRy_bbuRdD7d4OtCFrANb2gfteaLV7600_AzMbrOXk7cMe4x15fP1y7JOd1fJKvyeP5HrVjcsPDnR_ANJ8q8s |
| linkProvider | Elsevier |
| 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=Higher+order+approximation+to+the+Hill+problem+dynamics+about+the+libration+points&rft.jtitle=Communications+in+nonlinear+science+%26+numerical+simulation&rft.au=Lara%2C+Martin&rft.au=P%C3%A9rez%2C+Iv%C3%A1n+L.&rft.au=L%C3%B3pez%2C+Rosario&rft.date=2018-06-01&rft.issn=1007-5704&rft.volume=59&rft.spage=612&rft.epage=628&rft_id=info:doi/10.1016%2Fj.cnsns.2017.12.007&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cnsns_2017_12_007 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1007-5704&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1007-5704&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1007-5704&client=summon |