Families of periodic orbits in the restricted four-body problem

Baltagiannis, A.; Papadakis, K. E.

doi:10.1007/s10509-011-0778-7

Cited by 61 publications

(39 citation statements)

References 23 publications

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“…Thus, the traditional differential correction method which utilizes the symmetry of the trajectory as the terminal constrains is no longer applicable. 31,32 An improved multiple-shooting method is employed in this section to derive quasi-periodic trajectory. The general approach is represented as follows:…”

Section: Baseline Trajectory Designmentioning

confidence: 99%

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L₂ point

Qian

Liu²,

Zhang

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part G:

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Quasi-periodic orbits in the Earth-Moon system are highly sensitive and even small errors in position and/or velocity have strong influence on the trajectory. These types of trajectories are unstable and must be controlled to maintain the corresponding orbits. This paper investigates the stationkeeping strategy for quasi-periodic orbits near the translunar libration point with full consideration of the contribution from the Sun's gravity and the Moon's eccentricity, in which the continuous low-thrust is preformed to enforce the probe following several onboard decided target points on the baseline. A new high-fidelity model is derived to describe motions of the quasi-periodic orbits by using the standard ephemerides. Based on the improved multiple-shooting method and the proposed model, a baseline trajectory is obtained. Then, a new continuous low-thrust-based stationkeeping strategy is proposed. Specifically, by employing Gauss pseudospectral method in the stationkeeping algorithm and by introducing the maximal excursion and fixed time interval, the target points on the baseline trajectory are chosen onboard based on real-time data. Simulation results show that the unstable quasi-periodic orbit can be maintained effectively with the low-energy consumption.

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Section: Baseline Trajectory Designmentioning

confidence: 99%

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L₂ point

Qian

Liu²,

Zhang

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…The study of the existence of periodic orbits in the restricted four‐body problem fascinated many researchers in recent time: some of them are Alvarez‐Ramírez & Barrabés (), Baltagiannis & Papadakis (), Papadakis (), Burgaos‐Garcia & Delgado ()). Furthermore, the existence and stability of equilibrium points in the restricted four‐body problem are studied and presented in a series of research articles: Kumari & Kushvah (), Asique et al (), Asique et al (), Papadouris & Papadakis (), and Singh & Vincent ().…”

Section: Introductionmentioning

confidence: 99%

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

et al. 2019

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In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme.

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“…Similar to CR3BP, it has been analytically proved that the R4BP has some relative equilibrium solutions like the RTBP, and there are families of periodic orbits in the vicinity of equilibrium points [7]. The quasi-halo orbits in the SunEarth-Moon system were computed from the bicircular model in R4BP by Andreu [8].…”

Section: Introductionmentioning

confidence: 99%

“…Papadakis [9] computed the invariant stable and unstable manifolds in R4BP. For the Sun-Jupiter-Trojan asteroid-spacecraft system, the evolution of the families of periodic orbit and their stability around the asteroid and/or the Jupiter in R4BP were calculated by Baltagiannis and Papadakis [7,10]. The periodic orbits in the R4BP with two equal masses were explored by Burgos-García and Delgado [11].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series

Qian¹,

Yang²,

Yang³

et al. 2016

International Journal of Aerospace Engineering

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The restricted three-body problem (R3BP) and restricted four-body problem (R4BP) are modeled based on the rotating frame. The conservative autonomous system for the R3BP and nonautonomous system with period parametric resonance due to the fourth body are derived. From the vibrational point of view, the methodology of polynomial series is proposed to solve for these problems analytically. By introducing the polynomial series relations among the three directions of motion, the three-degree-of-freedom coupled equations are transferred into one degree-of-freedom containing the full dynamics of the original autonomous system for the R3BP. As for the R4BP case, the methodology of polynomial series combined with the iterative approach is proposed. During the iterative approach, the nonautonomous system can be treated as pseudoautonomous equation and the final polynomial series relations and one-degree-of-freedom system can be derived iteratively.

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Families of periodic orbits in the restricted four-body problem

Cited by 61 publications

References 23 publications

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L₂ point

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L₂ point

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series

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Families of periodic orbits in the restricted four-body problem

Cited by 61 publications

References 23 publications

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L2 point

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L2 point

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series

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Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L₂ point

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L₂ point