Relevant bibliographies by topics / Collinear Libration points

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  2. Dissertations / Theses
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Academic literature on the topic 'Collinear Libration points'

Author: Grafiati
Published: 5 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Collinear Libration points"

1

Muhammad, Amjad, Aslam Mohd., and Kashif Khan Mohd. "A MATHEMATICAL MODEL IN RESTRICTED THREE-BODY PROBLEM WHEN THE SMALLER PRIMARY IS A UNIFORM STRAIGHT ROD." International Journal of Education &Applied Sciences Research 1, no. 6 (2014): 07–20. https://doi.org/10.5281/zenodo.10686151.

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<strong>Abstract</strong> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <em>In this paper we have shown the existence of libration points in the restricted three-body problem when the smaller primary is a uniform straight rod. It is found that there exist five libration points out of which L<strong><sub>i</sub> </strong>(i=1, 2, 3) are collinear and L<sub>4, 5 </sub>are non-collinear .The collinear libration points are unstable for 0 &le; &micro; &le; &frac12; and 0 &lt; l &lt;1 while non-collinear libration points are stable for critical value of mass parameter &micro;<sub>c </sub>= 0.381410285&hellip;. and length parameter l<sub>c</sub> =0.4.&nbsp; </em> <strong><em>&nbsp;</em></strong> <strong><em>Key Words</em></strong><strong><em>: </em></strong><em>Celestial Mechanics</em><em>, Restricted three-body problem, Collinear Libration points,&nbsp;&nbsp; Non-collinear Libration Points, Stability of Libration points.</em>
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Idrisi, M. Javed. "A study of libration points in CR3BP under albedo effect." International Journal of Advanced Astronomy 5, no. 1 (2016): 1. http://dx.doi.org/10.14419/ijaa.v5i1.6852.

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In this paper this is investigated how albedo perturbed the libration points from its original position? It is found that there exist five libration points, three collinear and two non-collinear and all the libration points are affected by Albedo. The non-collinear libration points are stable for a critical value of mass parameter µ ≤ µc, where µc = µo − (0.00891747 + 0.222579k)α (µo is the critical mass parameter for classical case) but collinear libration points are still unstable.
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Idrisi, M. Javed, and Mamta Jain. "Restricted three-body problem with stokes drag effect when less massive primary is an ellipsoid." International Journal of Advanced Astronomy 4, no. 1 (2016): 61. http://dx.doi.org/10.14419/ijaa.v4i1.6140.

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The present paper deals with the effect of Stokes drag force on the existence and stability of collinear and non-collinear libration points in circular restricted three-body problem when less massive primary is an ellipsoid. During the investigation, it is found that there exist five libration points Li (i = 1, 2… 5) out of which three are collinear and two are non-collinear. We observed that the Stokes drag force does not affect the collinear libration points while non-collinear libration points are affected by it and all the libration points either collinear or non-collinear are unstable in Lyapunov sense for the given range of dissipative constant k and mass parameter µ.
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Idrisi, M. Javed, та Muhammad Amjad. "Effect of elliptic angle φ on the existence and stability of libration points in restricted three-body problem in earth-moon system considering earth as an ellipsoid". International Journal of Advanced Astronomy 3, № 2 (2015): 87. http://dx.doi.org/10.14419/ijaa.v3i2.5313.

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&lt;p&gt;This paper deals with the existence and the stability of the earth-moon libration points in the restricted three-body problem. In this paper we have considered the bigger primary as an ellipsoid while the smaller one as a point-mass. This is observed that the collinear and non-collinear libration points exist only in the interval 0˚&amp;lt;&lt;em&gt;φ &lt;/em&gt;&amp;lt; 45˚. There exist three collinear libration points and the non-collinear libration points are forming a right triangle with the primaries. Further observed that the libration points either collinear or non-collinear all are unstable in 0˚&amp;lt;&lt;em&gt;φ &lt;/em&gt;&amp;lt; 45˚.&lt;/p&gt;
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5

1M., Javed Idrisi, and Amjad Muhammad. "TWO MORE SOLUTIONS OF NON-COLLINEAR LIBRATION POINTS IN A PLANAR RESTRICTED THREE-BODY PROBLEM WHEN LESS MASSIVE PRIMARY IS AN OBLATE SPHEROID." International Journal of Education &Applied Sciences Research 2, no. 8 (2015): 01–14. https://doi.org/10.5281/zenodo.10691042.

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<strong>Abstract</strong> <em>In this paper the stability of non-collinear libration points in circular restricted three-body problem has been analyzed considering less massive primary as an oblate spheroid. We have considered two cases to find out the location and stability of non-collinear libration points. In case I, it is observed that there exist infinite numbers of non-collinear libration points on the unit circle centered at oblate body and out of these libration points only those lying in the interval&nbsp; 57˚ &le; &psi; &le; 60˚ are stable for different values of critical mass parameter &micro;<sub>c</sub>, where &psi; is the angle between m<sub>3</sub>, m<sub>2</sub> and m<sub>1</sub> in the same plane. In case II, </em><em>the non-collinear libration points exist only in the interval </em><em>0˚ &le; &phi; &le; 140˚ are stable for different values of critical mass parameter &micro;<sub>c</sub>, during the analysis<sub> </sub>we got a collinear libration point which is stable for &micro;<sub>c</sub> &le; </em><em>0.127284&hellip; .</em> <em>&nbsp;</em> <strong><em>Key Words:</em></strong><em> Celestial Mechanics, Restricted three-body problem, Libration points, Linear stability.</em>
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M., JAVED IDRISI. "EXISTENCE AND STABILITY OF NON-COLLINEAR LIBRATION POINTS IN RESTRICTED THREE-BODY PROBLEM WHEN SMALLER PRIMARY IS A PROLATE SPHEROID." International Journal of Education &Applied Sciences Research 2, no. 3 (2015): 01–08. https://doi.org/10.5281/zenodo.10687004.

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<strong>Abstract</strong> In this paper the existence and stability of &nbsp;non-collinear libration points in the restricted three-body problem has been discussed when the smaller primary is a prolate spheroid. We have determined the equations of motion of the infinitesimal mass and then we have investigated the non-collinear libration points and their stability in linear sense. This is found that there exist two non-collinear libration points are stable for a critical value of mass parameter&nbsp;&nbsp;&nbsp;&nbsp; <em>&nbsp;&micro;</em> = <em>&micro;<sub>c</sub></em> &le; 0.0559836. &nbsp; <strong>Key Words:</strong> Celestial Mechanics, Restricted three-body problem, Prolate Spheroid, Libration points, Linear Stability
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Hou, X. Y., and L. Liu. "Bifurcating families around collinear libration points." Celestial Mechanics and Dynamical Astronomy 116, no. 3 (2013): 241–63. http://dx.doi.org/10.1007/s10569-013-9485-8.

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Idrisi, M. Javed, and Kumari Shalini. "Non-collinear libration points in CR3BP when less massive primary is an heterogeneous oblate body with N-layers." International Journal of Advanced Astronomy 4, no. 1 (2016): 39. http://dx.doi.org/10.14419/ijaa.v4i1.5928.

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&lt;p&gt;In the present paper, the existence of non-collinear libration points has been shown in circular restricted three-body problem when less massive primary is a heterogeneous oblate body with N-layers. Further, the stability of non-collinear libration points is investigated in linear sense and found that the non-collinear libration points are stable for the critical value of mass parameter &lt;em&gt;µ&lt;/em&gt; ≤ &lt;em&gt;µ&lt;sub&gt;crit&lt;/sub&gt;&lt;/em&gt;= &lt;em&gt;µ&lt;/em&gt;&lt;sub&gt;o&lt;/sub&gt; – 3.32792 &lt;em&gt;k&lt;/em&gt;&lt;sub&gt;1&lt;/sub&gt; – 1.16808 &lt;em&gt;k&lt;/em&gt;&lt;sub&gt;2&lt;/sub&gt;.&lt;/p&gt;
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Abouelmagd, E. I., F. Alzahrani, A. Hobiny, J. L. G. Guirao, and M. Alhothuali. "Periodic orbits around the collinear libration points." Journal of Nonlinear Sciences and Applications 09, no. 04 (2016): 1716–27. http://dx.doi.org/10.22436/jnsa.009.04.27.

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Hou, X. Y., and L. Liu. "ON LYAPUNOV FAMILIES AROUND COLLINEAR LIBRATION POINTS." Astronomical Journal 137, no. 6 (2009): 4577–85. http://dx.doi.org/10.1088/0004-6256/137/6/4577.

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Dissertations / Theses on the topic "Collinear Libration points"

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Mondelo, González José María. "Contribution to the Study of Fourier Methods for Quasi-Periodical Functions and the Vicinity of the Collinear Libration Points." Doctoral thesis, Universitat de Barcelona, 2001. http://hdl.handle.net/10803/2106.

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This works has been organized in three parts. The first (Chapter 1 to 5) is dedicated to the development and study of a procedure for the accurate computation of frequencies, as well ans the related Fourier coefficients, of a quasi-periodical funcition. The second part of the work (Chapters 6 to 7) is devoted to the study to the dynamics in the vicinity of the collinear equilibrium points of the three-dimensional RTBP fo the Earth-Moon mass parameter. The third part consists in several appendices, which give some additional results that have been taken apart from the main text in order to improve its readability.
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Books on the topic "Collinear Libration points"

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Dynamics and Mission Design near Libration Points Vol. 1: Fundamentals - The Case of Collinear Libration Points. World Scientific Publishing Co Pte Ltd, 2001.

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Jorba, A., and J. Masdemont. Dynamics and Mission Design near Libration Points: Advanced Methods for Collinear Points. World Scientific Publishing Co Pte Ltd, 2001.

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Jorba, Angel, Carles Simo, and Josep Masdemont. Dynamics and Mission Design Near Libration Points, Vol. III, Advanced Methods for Collinear Points. World Scientific Publishing Company, 2001.

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Jorba, A., and J. Masdemont. Dynamics and Mission Design near Libration Points Vol. III: Advanced Methods for Collinear Points. World Scientific Publishing Co Pte Ltd, 2001.

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Simo, Carles, J. Llibre, and R. Martinex. Dynamics and Mission Design Near Libration Points, Volume I : Fundamentals : The Case of Collinear Libration Points (World Scientific Monograph Series in Mathematics). World Scientific Publishing Company, 2001.

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Dynamics and Mission Design Near Libration Points, Vol I: Fundamentals : The Case Of Collinear Libration Points (World Scientific Monograph Series in Mathematics). World Scientific Publishing, 2001.

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Dynamics and Mission Design near Libration Points : Volume I Fundamentals: The Case of Collinear Libration Points. World Scientific Monograph Series in Mathematics, Volume 2. World Scientific Publishing Co Pte Ltd, 2001.

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Book chapters on the topic "Collinear Libration points"

1

Gómez, Gerard, and José M. Mondelo. "The Central Manifold for the Collinear Libration Points." In Modern Celestial Mechanics: From Theory to Applications. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-2304-6_29.

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Simó, Carles. "Dynamical Systems Methods for Space Missions on a Vicinity of Collinear Libration Points." In Hamiltonian Systems with Three or More Degrees of Freedom. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4673-9_19.

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Olikara, Zubin P., Gerard Gómez, and Josep J. Masdemont. "A Note on Dynamics About the Coherent Sun–Earth–Moon Collinear Libration Points." In Astrodynamics Network AstroNet-II. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-23986-6_13.

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Shmyrov, Alexander, Vasily Shmyrov, and Dzmitry Shymanchuk. "Attitude Controlled Motion in a Neighborhood of the Collinear Libration Point $$L_1$$." In Lecture Notes in Control and Information Sciences - Proceedings. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-87966-2_54.

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"Expansions Required for the Equations of Motion: Collinear Points Case." In Dynamics and Mission Design Near Libration Points. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810632_0007.

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Conference papers on the topic "Collinear Libration points"

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Ghazy, Mohammed, and Brett Newman. "Transition Boundaries at the Collinear Libration Points." In AIAA/AAS Astrodynamics Specialist Conference. American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-7661.

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Eismont, Natan. "Optimal Transfer to Solar-Terrestrial Collinear Libration Points." In SpaceOps 2012. American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-1275783.

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Howell, K. "Families of orbits in the vicinity of the collinear libration points." In AIAA/AAS Astrodynamics Specialist Conference and Exhibit. American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-4465.

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Jennings, Donna, and Henry Pernicka. "Identifying Relative Trajectory Geometries at Collinear Libration Points Using Genetic Algorithms." In 2021 IEEE Aerospace Conference. IEEE, 2021. http://dx.doi.org/10.1109/aero50100.2021.9438189.

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Zhiqin Cai, Jun Zhao, Haijun Peng, and Zhaohui Qi. "Nonlinear station-keeping control of unstable orbits near collinear libration points." In 2010 3rd International Symposium on Systems and Control in Aeronautics and Astronautics (ISSCAA 2010). IEEE, 2010. http://dx.doi.org/10.1109/isscaa.2010.5632398.

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Jennings, Donna, and Henry Pernicka. "Numerical Determination of Natural Spacecraft Formations Near the Collinear Libration Points." In 2020 IEEE Aerospace Conference. IEEE, 2020. http://dx.doi.org/10.1109/aero47225.2020.9172690.

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Bermejo Ballesteros, Juan, José María Vergara Pérez, Alejandro Fernández Soler, and Javier Cubas Cano. "Mubody, an astrodynamics open-source Python library focused on libration points." In Symposium on Space Educational Activities (SSAE). Universitat Politècnica de Catalunya, 2022. http://dx.doi.org/10.5821/conference-9788419184405.040.

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Mubody is an astrodynamics open-source Python library focused on the libration points. Such points result from the equilibrium of the gravitational forces between two massive bodies as the Sun and Earth, for example. The library is mainly intended for the generation of orbits in these regions, which is not a straightforward process, specially if perturbations are considered. Currently, the library allows to generate Lissajous orbits in the second Lagrange point of the Sun-Earth system under the influence of perturbations such as the Earth orbit eccentricity. The next milestone, as a result of a master student work, is the incorporation of Halo orbits and the expansion to all three collinear libration points from any two massive bodies of the Solar System. This tool has been developed as part of a PhD, motivated by the need of performing mission analysis in libration point regions. Nevertheless, since its creation it has also proven to be an excellent academic tool for both enhancing the library itself and using its results for further studies (collision risk, thermal analysis, formation flight control, etc). As a result, the tool has rapidly evolved, building onto the knowledge and experience that the students gather while working on their academic projects (bachelor’s degree dissertations, master theses, subjects, internships). The participation on the library development provides students with experience in orbital mechanics, software design, version control and it compels them to ensure that their work can be readily used by others as it is properly documented. The project is hosted in GitLab under a MIT licence
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Lei, Liu, and Cao Jian-feng. "Design and stationkeeping of Lissajous trajectories about the Earth-Moon collinear libration points." In 2014 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC). IEEE, 2014. http://dx.doi.org/10.1109/cgncc.2014.7007552.

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EISMONT, N., A. SUKHANOV, and V. KHRAPCHENKOV. "TECHNICAL CONSTRAINTS IMPACT ON MISSION DESIGN TO THE COLLINEAR SUN–EARTH LIBRATION POINTS." In Proceedings of the Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704849_0004.

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Shmyrov, Alexander, and Dzmitry Shymanchuk. "Maneuvering in near-Earth space with the use of the collinear libration points." In 2015 International Conference on Mechanics-Seventh Polyakhov's Reading. IEEE, 2015. http://dx.doi.org/10.1109/polyakhov.2015.7106777.

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