On the quasi-equilibria of the BiElliptic four-body problem with non-coplanar motion of primaries

Assadian, Nima; Pourtakdoust, Seid H.

doi:10.1016/j.actaastro.2009.05.014

Cited by 28 publications

(11 citation statements)

References 27 publications

(36 reference statements)

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“…The vector equation ofBRFBP can be expressed in the rotatingframe asfollows [4] . The scalar formof the above BRFBP equations is given in Appendix.…”

Section: Fig1 the Relationship Between Different Bodiesmentioning

confidence: 99%

“…In recent years, low-cost libration orbit transfer attracts much attentions [1][2][3][4][5][6][7][8][9][10][11][12].The low-cost orbit transfer based on the restricted four-body model is implemented in the Earth-Moon systemin reference [1]. Howell and Kakoi [2] use invariant manifolds to study low-cost transfer trajectory between the Sun-Earth and the Earth-Moon systems.…”

Section: Introductionmentioning

confidence: 99%

“…Howell and Kakoi [2] use invariant manifolds to study low-cost transfer trajectory between the Sun-Earth and the Earth-Moon systems. The dynamic characteristics of the complex bielliptic four body problem is studied in reference [4].Pseudo-stable manifold is considered in reference [5] to contain the effect of the forth body, and then the transfer trajectory is determined using the low-thrust and the pseudo-stable manifold. Based on the multi-objective geneticalgorithm and calculus-of-variations-based low-thrust trajectory optimization, reference [6]designs the transfer trajectory between the Earth-Mars and the Earth-Mercury systems.Canalias and Masdemont [7] usethe coupled restricted three body model and the JPL ephemeris for analyzing the natural transfer orbits between the Sun-Earth and the Sun-Moon systems.…”

Section: Introductionmentioning

confidence: 99%

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A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun–Earth and the Earth–Moon systems

Wang

Peng

2017

Aerospace Science and Technology

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This paper considers the emergency trajectory design mission of libration point orbit transfer between the Sun-Earth system and the Earth-Moon system. In order to balance the two indexes of transfer time and fuel consumption, Halo orbits and theirinvariant manifolds in the circular restricted three body problem (CRTBP) are combined with low thrust in the bicircular restricted four body problem (BRFBP) to design the transfer trajectories. A fast multi-objective optimization methodbased on surrogate modelwhich is greatly needed especially for emergency transfer missions is proposedto overcome the low-efficacy of original evolutionary multi-objectiveoptimization methods. The advantages of the Sun-Earth manifolds,the Earth-Moon manifoldsand the optimal control methodare fully considered.In the part of numerical simulations, several simple problems with analytical solutions are first employed to validate the proposed fast optimization algorithm,thenthe proposed method is compared with NSGA-II for the same multi-objective transfer problem. Numerical results show that the fast optimization method chooses the expected samplesand has a much higher efficiency than direct multi-objective optimization. The significance of the Sun-Earth manifolds and the Earth-Moon manifolds are considered. Several cases show the complicated relationship between transfer time and fuel consumption.

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“…The vector equation ofBRFBP can be expressed in the rotatingframe asfollows [4] . The scalar formof the above BRFBP equations is given in Appendix.…”

Section: Fig1 the Relationship Between Different Bodiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun–Earth and the Earth–Moon systems

Wang

Peng

2017

Aerospace Science and Technology

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“…Assaidian and Pourtakdoust [19] studied the effect of the Sun on the libration points of the EarthMoon system with the bi-elliptical model. Oshima et al [20] studied the mechanism of gravity assist in the Sun-Earth-Moon-spacecraft system based on the bi-circular/bi-elliptical four-body problem model.…”

Section: Candiceqyj@163commentioning

confidence: 99%

Parametric stability analysis for planar bicircular restricted four-body problem

Qian

Yang

et al. 2018

Astrodyn

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“…在BCM基础上, Assadian和Pourtakdoust [10] 进一步提出了双椭圆模型(BiElliptic Problem, BEP [12] 和月球外侧的Halo轨道 [13] 等问题. 从QBCP的准周期Halo轨道出发, Andreu计算得到了时间超过41年的真实地月星历(Real Ephemeris, REMS)下的L 2 附近的Halo轨道 [14] .…”

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Quasi-bielliptic three-body problem

2020

Sci. Sin.-Phys. Mech. Astron.

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Articles you may be interested in Variational methods for the choreography solution to the three-body problem Science in China Series A-Mathematics 45, 594 (2002); Co-orbital restricted three-body problem and its application Chinese Science Bulletin 55, 1343 (2010); The co-orbital restricted three-body problem and its application SCIENCE CHINA Physics, Mechanics & Astronomy 53, 171 (2010); A novel method of periodic orbit computation in circular restricted three-body problem SCIENCE CHINA Technological Sciences 54, 2197 (2011); A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem

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On the quasi-equilibria of the BiElliptic four-body problem with non-coplanar motion of primaries

Cited by 28 publications

References 27 publications

A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun–Earth and the Earth–Moon systems

A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun–Earth and the Earth–Moon systems

Parametric stability analysis for planar bicircular restricted four-body problem

Quasi-bielliptic three-body problem

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