Search in:

Dynamical Systems

An International Journal

Volume 20, 2005 - Issue 1: Special issue on mechanics and space mission design Edited by Michael Dellnitz and Jerrold E. Marsden

Submit an article Journal homepage

520

Views

CrossRef citations to date

Altmetric

Original Articles

High-order expansions of invariant manifolds of libration point orbits with applications to mission design

J. J. Masdemont *View further author information

Pages 59-113 | Received 02 Jan 2004, Accepted 03 Aug 2004, Published online: 01 Oct 2010

Cite this article
https://doi.org/10.1080/14689360412331304291

Full Article
Figures & data
References
Citations
Metrics
Reprints & Permissions

Citations (73)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Articles from other publishers (73)

Massimiliano Guzzo & Elena Lega. (2023) Theory and applications of fast Lyapunov indicators to model problems of celestial mechanics. Celestial Mechanics and Dynamical Astronomy 135:4.
Crossref

Mingpei Lin, Jinxiu Zhang, Ming Xu & Xiao Pan. (2023) High-order analytical solutions of bounded relative motions for Coulomb formation flying. Nonlinear Dynamics 111:14, pages 12931-12946.
Crossref

Damennick B. Henry & Daniel J. Scheeres. (2023) Quasi-Periodic Orbit Transfer Design via Whisker Intersection Sets. Journal of Guidance, Control, and Dynamics, pages 1-16.
Crossref

Thomas Caleb, Matteo Losacco, Alberto Fossà, Roberto Armellin & Stéphanie Lizy-Destrez. (2023) Differential algebra methods applied to continuous abacus generation and bifurcation detection: application to periodic families of the Earth–Moon system. Nonlinear Dynamics 111:11, pages 9721-9740.
Crossref

Rocío I. Paez & Massimiliano Guzzo. (2022) On the semi-analytical construction of halo orbits and halo tubes in the elliptic restricted three-body problem. Physica D: Nonlinear Phenomena 439, pages 133402.
Crossref

Miao Li & Shengping Gong. (2022) Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism. Applied Sciences 12:13, pages 6530.
Crossref

Martin Lara. (2022) On perturbation solutions in the restricted three-body problem dynamics. Acta Astronautica 195, pages 596-604.
Crossref

Yang Jin & Bo Xu. (2022) Three-maneuver transfers from the cislunar halo orbits to low lunar orbits . Advances in Space Research 69:2, pages 989-999.
Crossref

Rocío I Paez & Massimiliano Guzzo. (2021) Transits close to the Lagrangian solutions L 1 , L 2 in the elliptic restricted three-body problem . Nonlinearity 34:9, pages 6417-6449.
Crossref

Sergey Aksenov, Stanislav Bober & Maria Guskova. (2021) Mapping of initial conditions for libration point orbits. Advances in Space Research 68:6, pages 2501-2514.
Crossref

Pan Tan, Xi-Yun Hou & Xin-Hao Liao. (2021) Explicit solution and resonance dynamics around triangular libration points of the planar elliptic restricted three-body problem. Celestial Mechanics and Dynamical Astronomy 133:7.
Crossref

Rocío I. Paez & Massimiliano Guzzo. (2020) A study of temporary captures and collisions in the Circular Restricted Three-Body Problem with normalizations of the Levi-Civita Hamiltonian. International Journal of Non-Linear Mechanics 120, pages 103417.
Crossref

Renato C Calleja, Alessandra Celletti & Rafael de la Llave. (2020) Existence of whiskered KAM tori of conformally symplectic systems. Nonlinearity 33:1, pages 538-597.
Crossref

Hanlun Lei. (2019) A semi-analytical model for secular dynamics of test particles in hierarchical triple systems. Monthly Notices of the Royal Astronomical Society 490:4, pages 4756-4769.
Crossref

Ying-Jing Qian, Jian-Yu Guo, Tian-Jun Yu, Xiao-Dong Yang & Dong-Mei Wang. (2019) Halo orbits construction based on invariant manifold technique. Acta Astronautica 163, pages 24-37.
Crossref

Yue Zheng, Binfeng Pan & Shuo Tang. (2019) A hybrid method based on invariant manifold and chaos control for earth-moon low-energy transfer. Acta Astronautica 163, pages 145-156.
Crossref

Yang Jin & Bo Xu. (2019) A Modified Targeting Strategy for Station-Keeping of Libration Point Orbits in the Real Earth-Moon System. International Journal of Aerospace Engineering 2019, pages 1-11.
Crossref

Ying-Jing Qian, Xiao-Dong Yang, Guan-Qiao Zhai & Wei Zhang. (2017) Planar periodic orbits’ construction around libration points with invariant manifold technique. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233:2, pages 498-509.
Crossref

Rafael de la Llave & Florian Kogelbauer. (2019) Global Persistence of Lyapunov Subcenter Manifolds as Spectral Submanifolds under Dissipative Perturbations. SIAM Journal on Applied Dynamical Systems 18:4, pages 2099-2142.
Crossref

Josep-Maria Mondelo. 2019. Satellite Dynamics and Space Missions. Satellite Dynamics and Space Missions 159 223 .

Qiwei Guo, Hanlun Lei & Bo Xu. (2018) Semianalytical Solutions of Relative Motions with Applications to Periodic Orbits about a Nominal Circular Orbit. Mathematical Problems in Engineering 2018, pages 1-14.
Crossref

Yuying Liang, Ming Xu & Shijie Xu. (2018) High-order solutions of motion near triangular libration points for arbitrary value of $${\varvec{\mu }}$$ μ. Nonlinear Dynamics 93:2, pages 909-932.
Crossref

Stefano Carletta, Mauro Pontani & Paolo Teofilatto. (2018) Long-term capture orbits for low-energy space missions. Celestial Mechanics and Dynamical Astronomy 130:7.
Crossref

Massimiliano Guzzo & Elena Lega. (2018) Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem. Physica D: Nonlinear Phenomena 373, pages 38-58.
Crossref

Martin Lara, Iván L. Pérez & Rosario López. (2018) Higher order approximation to the Hill problem dynamics about the libration points. Communications in Nonlinear Science and Numerical Simulation 59, pages 612-628.
Crossref

Yingjing QIAN, Xiaodong YANG, Wuxing JING & Wei ZHANG. (2018) An improved numerical method for constructing Halo/Lissajous orbits in a full solar system model. Chinese Journal of Aeronautics 31:6, pages 1362-1374.
Crossref

Hanlun Lei, Bo Xu & Christian Circi. (2018) Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem. Celestial Mechanics and Dynamical Astronomy 130:5.
Crossref

Xiyun Hou & Xiaosheng Xin. (2017) A note on the full two-body problem and related restricted full three-body problem. Astrodynamics 2:1, pages 39-52.
Crossref

Ying-Jing Qian, Xiao-Dong Yang, Wei Zhang & Guan-Qiao Zhai. (2017) Periodic motion analysis around the libration points by polynomial expansion method in planar circular restricted three-body problem. Nonlinear Dynamics 91:1, pages 39-54.
Crossref

Vineet K. Srivastava, Jai Kumar & Badam Singh Kushvah. (2017) Halo orbit transfer trajectory design using invariant manifold in the Sun-Earth system accounting radiation pressure and oblateness. Astrophysics and Space Science 363:1.
Crossref

J. D. Mireles James & Maxime Murray. (2017) Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications. International Journal of Bifurcation and Chaos 27:14, pages 1730050.
Crossref

Martin Lara. (2017) A Hopf variables view on the libration points dynamics. Celestial Mechanics and Dynamical Astronomy 129:3, pages 285-306.
Crossref

B Le Bihan, J J Masdemont, G G?mez & S Lizy-Destrez. (2017) Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method. Nonlinearity 30:8, pages 3040-3075.
Crossref

Mauro Pontani & Paolo Teofilatto. (2017) Invariant manifold connections via polyhedral representation. Acta Astronautica 137, pages 512-521.
Crossref

Ying-Jing Qian, Xiao-Dong Yang, Guan-Qiao Zhai & Wei Zhang. (2017) Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions. Astrophysics and Space Science 362:8.
Crossref

Hanlun Lei & Bo Xu. (2017) Invariant manifolds around artificial equilibrium points for low-thrust propulsion spacecraft. Astrophysics and Space Science 362:4.
Crossref

J. L. Gonzalez & J. D. Mireles James. (2017) High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps. SIAM Journal on Applied Dynamical Systems 16:3, pages 1748-1795.
Crossref

Amadeu Delshams, Marian Gidea & Pablo Roldan. (2016) Arnold’s mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument. Physica D: Nonlinear Phenomena 334, pages 29-48.
Crossref

Lei Zhang & Bo Xu. (2016) Architecture analysis of the simplified libration point satellite navigation system. Advances in Space Research 58:7, pages 1275-1287.
Crossref

Hanlun Lei & Bo Xu. (2016) Families of impulsive transfers between libration points in the restricted three-body problem. Monthly Notices of the Royal Astronomical Society 461:2, pages 1786-1803.
Crossref

Hanlun Lei & Bo Xu. (2015) Transfers between libration point orbits of Sun?Earth and Earth?Moon systems by using invariant manifolds. Journal of Engineering Mathematics 98:1, pages 163-186.
Crossref

Amanda F. Haapala & Kathleen C. Howell. (2016) A Framework for Constructing Transfers Linking Periodic Libration Point Orbits in the Spatial Circular Restricted Three-Body Problem. International Journal of Bifurcation and Chaos 26:05, pages 1630013.
Crossref

F. Topputo. (2016) Fast numerical approximation of invariant manifolds in the circular restricted three-body problem. Communications in Nonlinear Science and Numerical Simulation 32, pages 89-98.
Crossref

Mauro Pontani & Paolo Teofilatto. (2016) Polyhedral representation of invariant manifolds applied to orbit transfers in the Earth?Moon system. Acta Astronautica 119, pages 218-232.
Crossref

Weipeng Li & Hai Huang. (2016) Optimization of low-thrust transfers to libration point orbits. Aircraft Engineering and Aerospace Technology 88:1, pages 16-23.
Crossref

Ivan Sergeevich Ilyin & Andrey Georgievich Tuchin. (2016) Quasiperiodic orbits near Sun-Earth L<sub>1</sub> libration point. Keldysh Institute Preprints:6, pages 1-28.
Crossref

Richard Epenoy. 2016. Recent Advances in Celestial and Space Mechanics. Recent Advances in Celestial and Space Mechanics 143 178 .

Hanlun Lei & Bo Xu. (2015) Analytical study on the motions around equilibrium points of restricted four-body problem. Communications in Nonlinear Science and Numerical Simulation 29:1-3, pages 441-458.
Crossref

Yijun Lian, Yudong Gao & Guojian Tang. (2015) On equatorial inclination of parking orbits in transfers to lunar halo orbits. Communications in Nonlinear Science and Numerical Simulation 28:1-3, pages 210-222.
Crossref

M. Zamaro & J. D. Biggs. (2015) Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics. Celestial Mechanics and Dynamical Astronomy 122:3, pages 263-302.
Crossref

Lei Liu, Jian-feng Cao, Yong Liu, Song-jie Hu, Ge-shi Tang & Jian-feng Xie. (2015) CHANG?E-3 contingency scheme and trajectory. Advances in Space Research 55:4, pages 1074-1084.
Crossref

Yijun Lian, Gerard Gómez, Josep J. Masdemont & Guojian Tang. (2014) Station-keeping of real Earth–Moon libration point orbits using discrete-time sliding mode control. Communications in Nonlinear Science and Numerical Simulation 19:10, pages 3792-3807.
Crossref

Hanlun Lei & Bo Xu. (2014) High-order solutions around triangular libration points in the elliptic restricted three-body problem and applications to low energy transfers. Communications in Nonlinear Science and Numerical Simulation 19:9, pages 3374-3398.
Crossref

Yuan Ren & Jinjun Shan. (2014) A novel algorithm for generating libration point orbits about the collinear points. Celestial Mechanics and Dynamical Astronomy 120:1, pages 57-75.
Crossref

Hanlun Lei, Bo Xu, Xiyun Hou & Yisui Sun. (2013) High-order solutions of invariant manifolds associated with libration point orbits in the elliptic restricted three-body system. Celestial Mechanics and Dynamical Astronomy 117:4, pages 349-384.
Crossref

Hanlun Lei & Bo Xu. (2013) High-order analytical solutions around triangular libration points in the circular restricted three-body problem. Monthly Notices of the Royal Astronomical Society 434:2, pages 1376-1386.
Crossref

Yijun Lian, Gerard G?mez, Josep J. Masdemont & Guojian Tang. (2013) A note on the dynamics around the Lagrange collinear points of the Earth?Moon system in a complete Solar System model. Celestial Mechanics and Dynamical Astronomy 115:2, pages 185-211.
Crossref

R. C. Calleja, E. J. Doedel, A. R. Humphries, A. Lemus-Rodr?guez & E. B. Oldeman. (2012) Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem. Celestial Mechanics and Dynamical Astronomy 114:1-2, pages 77-106.
Crossref

Jing L?Junfeng Li, Qishao Lu & Hexi Baoyin. (2012) Periodic orbits based on geometric structure of center manifold around Lagrange points. Astrophysics and Space Science 340:1, pages 17-25.
Crossref

Gregory Lantoine & Ryan P. Russell. (2013) Near Ballistic Halo-to-Halo Transfers between Planetary Moons. The Journal of the Astronautical Sciences 58:3, pages 335-363.
Crossref

Josep J. Masdemont. 2011. Nonlinear Science and Complexity. Nonlinear Science and Complexity 139 146 .

Elisa Maria Alessi, Gerard Gómez & Josep J. Masdemont. 2011. Nonlinear Science and Complexity. Nonlinear Science and Complexity 107 114 .

Elisa Maria Alessi, Gerard Gómez & Josep J. Masdemont. (2010) A motivating exploration on lunar craters and low-energy dynamics in the Earth–Moon system. Celestial Mechanics and Dynamical Astronomy 107:1-2, pages 187-207.
Crossref

Miguel Belló, Gerard Gómez & Josep J. Masdemont. 2010. Space Manifold Dynamics. Space Manifold Dynamics 1 96 .

Ernest Fontich, Rafael de la Llave & Yannick Sire. (2009) Construction of invariant whiskered tori by a parameterization method. Part I: Maps and flows in finite dimensions. Journal of Differential Equations 246:8, pages 3136-3213.
Crossref

P. Di Lizia, R. Armellin & M. Lavagna. (2008) Application of high order expansions of two-point boundary value problems to astrodynamics. Celestial Mechanics and Dynamical Astronomy 102:4, pages 355-375.
Crossref

Elisabet Canalias & Josep J. Masdemont. (2008) Computing natural transfers between Sun?Earth and Earth?Moon Lissajous libration point orbits. Acta Astronautica 63:1-4, pages 238-248.
Crossref

MARIAN GIDEA & JOSEP J. MASDEMONT. (2011) GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM. International Journal of Bifurcation and Chaos 17:04, pages 1151-1169.
Crossref

Roberto Armellin & Francesco Topputo. (2006) A sixth-order accurate scheme for solving two-point boundary value problems in astrodynamics. Celestial Mechanics and Dynamical Astronomy 96:3-4, pages 289-309.
Crossref

E. Canalias, A. Delshams, J. J. Masdemont & P. Roldán. (2006) The scattering map in the planar restricted three body problem. Celestial Mechanics and Dynamical Astronomy 95:1-4, pages 155-171.
Crossref

M. Romero-Gómez, J. J. Masdemont, E. Athanassoula & C. García-Gómez. (2006) The origin of rR 1 ring structures in barred galaxies . Astronomy & Astrophysics 453:1, pages 39-45.
Crossref

G. Gómez & M. Marcote. (2006) High-order Analytical Solutions of Hill’s Equations. Celestial Mechanics and Dynamical Astronomy 94:2, pages 197-211.
Crossref

E. Canalias, A. Delshams, J. J. Masdemont & P. Roldán. 2006. Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications. Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications 155 171 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.

People also read
Recommended articles
Cited by

To cite this article:

Reference style: APA Chicago Harvard

Citation copied to clipboard

Reference styles above use APA (6th edition), Chicago (16th edition) & Harvard (10th edition)

Download citation

Download a citation file in RIS format that can be imported by citation management software including EndNote, ProCite, RefWorks and Reference Manager.

Choose format: RIS BibTex RefWorks Direct Export

Choose options: Citation Citation & abstract Citation & references

High-order expansions of invariant manifolds of libration point orbits with applications to mission design

Articles from other publishers (73)

Information for

Open access

Opportunities

Help and information

Your download is now in progress and you may close this window

Login or register to access this feature

High-order expansions of invariant manifolds of libration point orbits with applications to mission design

Citations (73)

Articles from other publishers (73)

Reprints and Corporate Permissions

Academic Permissions

Related research

To cite this article:

Download citation

Information for

Open access

Opportunities

Help and information

Keep up to date