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Journal articles on the topic 'Circular Restricted Three Body Problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Dionysiou, D. D., and D. A. Vaiopoulos. "On the restricted circular three-charged-body problem." Astrophysics and Space Science 135, no. 2 (1987): 253–60. http://dx.doi.org/10.1007/bf00641560.

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2

Vrbik, Jan. "Chaos in Planar, Circular, Restricted Three-Body Problem." Applied Mathematics 04, no. 01 (2013): 40–45. http://dx.doi.org/10.4236/am.2013.41008.

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3

Abouelmagd, Elbaz I., Juan Luis García Guirao, and Jaume Llibre. "Periodic Orbits of Quantised Restricted Three-Body Problem." Universe 9, no. 3 (2023): 149. http://dx.doi.org/10.3390/universe9030149.

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In this paper, perturbed third-body motion is considered under quantum corrections to analyse the existence of periodic orbits. These orbits are studied through two approaches to identify the first (second) periodic-orbit types. The essential conditions are given in order to prove that the circular (elliptical) periodic orbits of the rotating Kepler problem (RKP) can continue to the perturbed motion of the third body under quantum corrections where a massive primary body has excessive gravitational force over the smaller primary body. The primaries moved around each other in circular (elliptic

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4

Minglibayev, M. Zh, and T. M. Zhumabek. "ON THE RESTRICTED THREE-BODY PROBLEM." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (2021): 138–44. http://dx.doi.org/10.32014/2021.2518-1726.33.

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The paper analytically investigates the classical restricted three-body problem in a special non-inertial central coordinate system, with the origin at center of forces. In this coordinate system, an analytical expression of the invariant of the centre of forces is given. The existence of the invariant of the centre of forces admits the correct division of the problem into two problems. The first is a triangular restricted three-body problem. The second is a collinear restricted three-body problem. In this paper the collinear restricted three-body problem is investigated. Using the properties

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5

Campagnola, Stefano, Paul Skerritt, and Ryan P. Russell. "Flybys in the planar, circular, restricted, three-body problem." Celestial Mechanics and Dynamical Astronomy 113, no. 3 (2012): 343–68. http://dx.doi.org/10.1007/s10569-012-9427-x.

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6

Rodica, Roman, and Mioc Vasile. "Libration Points in Schwarzschild's Circular Restricted Three-Body Problem." Astrophysics and Space Science 304, no. 1-4 (2006): 101–3. http://dx.doi.org/10.1007/s10509-006-9083-2.

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7

Guzzetti, Davide, and Kathleen Connor Howell. "Attitude dynamics in the circular restricted three-body problem." Astrodynamics 2, no. 2 (2018): 87–119. http://dx.doi.org/10.1007/s42064-017-0012-7.

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8

Palacián, J. F., C. Vidal, J. Vidarte, and P. Yanguas. "Dynamics in the Charged Restricted Circular Three-Body Problem." Journal of Dynamics and Differential Equations 30, no. 4 (2017): 1757–74. http://dx.doi.org/10.1007/s10884-017-9627-x.

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9

Singh, Jagadish, and Achonu Joseph Omale. "Robe’s circular restricted three-body problem with zonal harmonics." Astrophysics and Space Science 353, no. 1 (2014): 89–96. http://dx.doi.org/10.1007/s10509-014-1995-7.

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10

Abduljabar Ansari, Abdullah, and Mehtab Alam. "Dynamics in the circular restricted three body problem with perturbations." International Journal of Advanced Astronomy 5, no. 1 (2017): 19. http://dx.doi.org/10.14419/ijaa.v5i1.7102.

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This paper presents the dynamics in the restricted problem with perturbations i.e. the circular restricted three body problem by considering one of the primaries as oblate and other one having the solar radiation pressure and all the masses are variable (primaries and infinitesimal body). For finding the autonomized equations of motion, we have used the Meshcherskii transformation. We have drawn the libration points, the time series, the zero velocity curves and Poincare surface of sections for the different values of the oblateness and solar radiation pressure. Finally, we have examined the s

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11

Kholshevnikov, Konstantin V., and Vladimir B. Titov. "Minimal velocity surface in the restricted circular Three-Body-Problem." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 65, no. 4 (2020): 734–42. http://dx.doi.org/10.21638/spbu01.2020.413.

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In the framework of the restricted circular Three-Body-Problem, the concept of the minimum velocity surface S is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of Hill surface requires occurrence of the Jacobi integral. The minimum velocity surface, other than the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of the main bodies motion. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained a

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12

Kholshevnikov, K. V., and V. B. Titov. "Minimal Velocity Surface in a Restricted Circular Three-Body Problem." Vestnik St. Petersburg University, Mathematics 53, no. 4 (2020): 473–79. http://dx.doi.org/10.1134/s106345412004007x.

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13

Makó, Zoltán, and Ferenc Szenkovits. "Capture in the Circular and Elliptic Restricted Three-Body Problem." Celestial Mechanics and Dynamical Astronomy 90, no. 1-2 (2004): 51–58. http://dx.doi.org/10.1007/s10569-004-5899-7.

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14

Guardia, Marcel, Pau Martín, and Tere M. Seara. "Oscillatory motions for the restricted planar circular three body problem." Inventiones mathematicae 203, no. 2 (2015): 417–92. http://dx.doi.org/10.1007/s00222-015-0591-y.

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15

Singh, J., and T. O. Amuda. "Perturbation effects in the generalized circular restricted three-body problem." Indian Journal of Physics 92, no. 11 (2018): 1347–55. http://dx.doi.org/10.1007/s12648-018-1227-z.

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16

Moreno, Agustin. "The circular restricted three-body problem: a modern symplectic viewpoint." European Mathematical Society Magazine, no. 135 (May 12, 2025): 33–38. https://doi.org/10.4171/mag/227.

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We give an overview of recent advances on the circular restricted three-body problem, from the perspective of modern symplectic geometry, and describe a “symplectic toolkit” created in connection to spacecraft trajectory design. This is based on the author’s recent book draft.

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17

Kumar, Prashant, and Susmitha C. "Study the Structure of Phase Space in the Frame Work of Planar Circular Restricted Three-Body Problem." Open Access Journal of Astronomy 2, no. 2 (2024): 1–7. http://dx.doi.org/10.23880/oaja-16000120.

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The numerical technique of Poincare surface of sections is used to create the surface of sections and to investigate the stability of the phase plane in various systems. This includes investigating the dependence of mass ratio and amplitude of stability areas in the Sun-Jupiter, Sun-Mercury, Sun-Io, and Sun-Uranus systems on the Jacobi constant. The amplitude of the stability areas diminishes with decreasing mass ratio. The phase plane structure differs for smaller mass ratios than it does for larger mass ratios.

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18

Bardin, B. S., and A. N. Avdyushkin. "On Stability of the Collinear Libration Point $L_{1}$ in the Planar Restricted Circular Photogravitational Three-Body Problem." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221202.

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The stability of the collinear libration point $L_{1}$ in the photogravitational three-body problem is investigated. This problem is concerned with the motion of a body of infinitely small mass which experiences gravitational forces and repulsive forces of radiation pressure coming from two massive bodies. It is assumed that the massive bodies move in circular orbits and that the body of small mass is located in the plane of their motion. Using methods of normal forms and KAM theory, a rigorous analysis of the Lyapunov stability of the collinear libration point lying on the segment connecting

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19

Koksin, Alexey M., and Vladimir A. Shefer. "Variational Chaos Indicators: Application to the Restricted Three-Body Problem." Proceedings of the International Astronomical Union 9, S310 (2014): 35–38. http://dx.doi.org/10.1017/s1743921314007777.

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AbstractA comparison of several known dynamical indicators of chaos based on the numerical integration of differential variational equations is performed. The comparison is implemented on the examples of studying dynamics in the planar circular restricted three-body problem.

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20

Tu, Xiongbiao, Qiao Wang, and Yifa Tang. "Highly Efficient Numerical Integrator for the Circular Restricted Three-Body Problem." Symmetry 14, no. 9 (2022): 1769. http://dx.doi.org/10.3390/sym14091769.

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The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such an integrator is more efficient than the symplectic Euler method and the Gauss Runge–Kutta method as regards this problem. In addition, we proved the integrator is symplectic by the discrete Hamilton’s principle. Several groups of numerical experiments demonstrated the precision and high efficiency of the integrator in the

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21

Abouelmagd, Elbaz I., Juan Luis García Guirao, and Jaume Llibre. "On the Periodic Orbits of the Perturbed Two- and Three-Body Problems." Galaxies 11, no. 2 (2023): 58. http://dx.doi.org/10.3390/galaxies11020058.

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In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies. Thus, we have proved that the first and second types of periodic orbits of the rotating Kepler problem can persist for all perturbed two-body and circular restricted three-body problems when the perturbation forces are conservative or the perturbed motion has its own extended Jacobian integral.

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22

Bando, Mai, and Akira Ichikawa. "Formation Flying Along Halo Orbit of Circular-Restricted Three-Body Problem." Journal of Guidance, Control, and Dynamics 38, no. 1 (2015): 123–29. http://dx.doi.org/10.2514/1.g000463.

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23

Aziz, Jonathan D., Daniel J. Scheeres, and Gregory Lantoine. "Hybrid Differential Dynamic Programming in the Circular Restricted Three-Body Problem." Journal of Guidance, Control, and Dynamics 42, no. 5 (2019): 963–75. http://dx.doi.org/10.2514/1.g003617.

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24

Luk’yanov, L. G. "On the restricted circular conservative three-body problem with variable masses." Astronomy Letters 35, no. 5 (2009): 349–59. http://dx.doi.org/10.1134/s1063773709050107.

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25

Singh, Jagadish, and Veronica Ugbedeojo Cyril-Okeme. "Perturbed Robe’s circular restricted three-body problem under an Oblate Primary." New Astronomy 34 (January 2015): 114–19. http://dx.doi.org/10.1016/j.newast.2014.06.006.

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26

Suraj, Md Sanam, Rajiv Aggarwal, Md Chand Asique, and Amit Mittal. "On the modified circular restricted three-body problem with variable mass." New Astronomy 84 (April 2021): 101510. http://dx.doi.org/10.1016/j.newast.2020.101510.

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27

Palacián, J. F., and P. Yanguas. "From the circular to the spatial elliptic restricted three-body problem." Celestial Mechanics and Dynamical Astronomy 95, no. 1-4 (2006): 81–99. http://dx.doi.org/10.1007/s10569-006-9023-z.

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28

Caillau, J. B., B. Daoud, and J. Gergaud. "Minimum fuel control of the planar circular restricted three-body problem." Celestial Mechanics and Dynamical Astronomy 114, no. 1-2 (2012): 137–50. http://dx.doi.org/10.1007/s10569-012-9443-x.

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29

Singh, Jagadish, and Hafsah Laraba Mohammed. "Robe’s Circular Restricted Three-Body Problem Under Oblate and Triaxial Primaries." Earth, Moon, and Planets 109, no. 1-4 (2012): 1–11. http://dx.doi.org/10.1007/s11038-012-9397-8.

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30

Murray, Carl D. "Dynamical Effects of Drag in the Circular Restricted Three-Body Problem." Icarus 112, no. 2 (1994): 465–84. http://dx.doi.org/10.1006/icar.1994.1198.

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31

Krasilnikov, P. S., and A. V. Dobroslavskiy. "AVERAGED CIRCULAR SPATIAL RESTRICTED THREE-BODY PROBLEM: INTERNAL CASE, NEW RESULTS." Доклады Российской академии наук. Математика, информатика, процессы управления 512, no. 1 (2023): 33–41. http://dx.doi.org/10.31857/s2686954323600489.

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We investigate the spatial restricted circular three-body problem in the nonresonant case. Namely, we apply Gaussian averaging to obtain averaged equations in terms of osculating elements and then investigate them. Keplerian ellipse with a focus in the main body (the Sun) is taken as an unperturbed orbit assuming the semi-major axis of the ellipse to be less than the radius of the orbit of the outer planet (internal problem). Using the Parseval formula we have derived the twice-averaged perturbed force function of the problem in the form of an explicit analytical series with coefficients expre

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32

Mandyam N Anandaram, Jeremy B. Tatum. "Orbits of Minor Bodies of the Solar System in the Circular Restricted Three-Body Problem." Mapana - Journal of Sciences 13, no. 1 (2017): 29–48. http://dx.doi.org/10.12723/mjs.28.3.

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A brief introduction to the circular restricted three-body problem (CR3BP) is given where a third body of negligible mass moves under the combined gravitational- centrifugal potential of two co-rotating massive bodies restricted to circular orbits. The equipotential contours of a variety of two body systems in the solar system are presented along with interesting orbits of Trojans, Hildas, Thule in the Sun-Jupiter system, the libration of Pluto in the Sun-Neptune system and choreographic orbits.

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33

ANTONIADOU, K. I., G. VOYATZIS, and T. KOTOULAS. "ON THE BIFURCATION AND CONTINUATION OF PERIODIC ORBITS IN THE THREE BODY PROBLEM." International Journal of Bifurcation and Chaos 21, no. 08 (2011): 2211–19. http://dx.doi.org/10.1142/s0218127411029720.

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We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only in particular resonances called "asymmetric resonances". However, numerical studies showed that in the general three body problem, asymmetric orbits may exist not only for asymmetric resonances, but for other kinds, too. In this work, we show the existence of asymmetric periodic orbits in the elliptic restricted problem. These families of periodic orbits co

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34

Álvarez-Ramírez, Martha, and Claudio Vidal. "Dynamical Aspects of an Equilateral Restricted Four-Body Problem." Mathematical Problems in Engineering 2009 (2009): 1–23. http://dx.doi.org/10.1155/2009/181360.

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The spatial equilateral restricted four-body problem (ERFBP) is a four body problem where a mass point of negligible mass is moving under the Newtonian gravitational attraction of three positive masses (called the primaries) which move on circular periodic orbits around their center of mass fixed at the origin of the coordinate system such that their configuration is always an equilateral triangle. Since fourth mass is small, it does not affect the motion of the three primaries. In our model we assume that the two masses of the primariesm2andm3are equal toμand the massm1is1−2μ. The Hamiltonian

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35

Korneev, Alexander, and Sergey Aksenov. "Calculation of libration point orbits in the circular restricted three-body problem." Journal of Physics: Conference Series 1740 (January 2021): 012019. http://dx.doi.org/10.1088/1742-6596/1740/1/012019.

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36

BANDO, Mai, Koichi OSUKA, Takao FUJII, and Hiroshi YAMAKAWA. "Implicit Control Structure in Lagrangian Points of Circular-restricted Three-body Problem." Transactions of the Society of Instrument and Control Engineers 48, no. 7 (2012): 431–40. http://dx.doi.org/10.9746/sicetr.48.431.

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37

K. "Discovery of an Equilibrium Circle in the Circular Restricted Three Body Problem." American Journal of Applied Sciences 9, no. 9 (2012): 1378–84. http://dx.doi.org/10.3844/ajassp.2012.1378.1384.

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38

Kholshevnikov, K. V., and V. B. Titov. "Erratum to: Minimal Velocity Surface in a Restricted Circular Three-Body Problem." Vestnik St. Petersburg University, Mathematics 54, no. 1 (2021): 111. http://dx.doi.org/10.1134/s1063454121010143.

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39

Ugai, Shin, and Akira Ichikawa. "Lunar Synchronous Orbits in the Earth-Moon Circular-Restricted Three-Body Problem." Journal of Guidance, Control, and Dynamics 33, no. 3 (2010): 995–1000. http://dx.doi.org/10.2514/1.47249.

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40

Zhang, Chen, Francesco Topputo, Franco Bernelli-Zazzera, and Yu-Shan Zhao. "Low-Thrust Minimum-Fuel Optimization in the Circular Restricted Three-Body Problem." Journal of Guidance, Control, and Dynamics 38, no. 8 (2015): 1501–10. http://dx.doi.org/10.2514/1.g001080.

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41

Gao, F. B., and W. Zhang. "A STUDY ON PERIODIC SOLUTIONS FOR THE CIRCULAR RESTRICTED THREE-BODY PROBLEM." Astronomical Journal 148, no. 6 (2014): 116. http://dx.doi.org/10.1088/0004-6256/148/6/116.

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42

GIDEA, MARIAN, and JOSEP J. MASDEMONT. "GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM." International Journal of Bifurcation and Chaos 17, no. 04 (2007): 1151–69. http://dx.doi.org/10.1142/s0218127407017744.

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The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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43

Beletsky, V. V., and A. V. Rodnikov. "Stability of triangle libration points in generalized restricted circular three-body problem." Cosmic Research 46, no. 1 (2008): 40–48. http://dx.doi.org/10.1134/s0010952508010061.

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44

Anderson, Rodney L., Robert W. Easton, and Martin W. Lo. "Isolating blocks as computational tools in the circular restricted three-body problem." Physica D: Nonlinear Phenomena 343 (March 2017): 38–50. http://dx.doi.org/10.1016/j.physd.2016.10.004.

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45

Zaborsky, Sergey. "Generating Solutions for Periodic Orbits in the Circular Restricted Three-Body Problem." Journal of the Astronautical Sciences 67, no. 4 (2020): 1300–1319. http://dx.doi.org/10.1007/s40295-020-00222-3.

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46

Roman, R., and I. Szücs-Csillik. "Regularization of the circular restricted three-body problem using ‘similar’ coordinate systems." Astrophysics and Space Science 338, no. 2 (2011): 233–43. http://dx.doi.org/10.1007/s10509-011-0899-z.

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47

Zotos, Euaggelos E. "Investigating the planar circular restricted three-body problem with strong gravitational field." Meccanica 52, no. 9 (2016): 1995–2021. http://dx.doi.org/10.1007/s11012-016-0548-2.

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48

Wei-Tao, Lu, Zhang Hua, and Wang Shun-Jin. "Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem." Chinese Physics Letters 25, no. 7 (2008): 2342–45. http://dx.doi.org/10.1088/0256-307x/25/7/004.

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49

Alhussain, Ziyad A. "THE YARKOVSKY EFFECT ON THE CIRCULAR RESTRICTED THREE-BODY PROBLEM WITH PERTURBATIONS." Advances in Differential Equations and Control Processes 19, no. 3 (2018): 153–68. http://dx.doi.org/10.17654/de019030153.

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50

Dionysiou, D. D., and G. G. Stamou. "Stability of motion of the restricted circular and charged three-body problem." Astrophysics and Space Science 152, no. 1 (1989): 1–8. http://dx.doi.org/10.1007/bf00645980.

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