Stable periodic orbits about the sun perturbed earth-moon triangularpoints.

Carpenter, L.; Kolenkiewicz, R.

doi:10.2514/3.4738

Cited by 25 publications

(3 citation statements)

References 3 publications

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“…Of particular interest was the existence of such motions in the presence of the Sun's gravitational perturbations. In [25], Schechter predicted the existence of coplanar periodic orbits in the Sun perturbed system which was later verified by the analysis of Kolenkiewicz and Carpenter [41].…”

Section: Dynamics Stability and Periodic Orbitsmentioning

confidence: 84%

Formation-Keeping Strategies At The Earth-Moon L4 Triangular Libration Point

Wong¹

2021

Preprint

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This thesis examines the use of thrusters and solar sails for spacecraft formation keeping control at the Earth-Moon L4 point. Particular emphasis was placed on the study of underactuated control, in which fewer control inputs than the system's degrees of freedom are available. A linear LQR control scheme, an integral augmented sliding mode controller and a bang-bang controller were applied to the dynamic spacecraft system. The nonlinear controllers produced errors falling with tighter tolerances than the linear controllers in the perturbed environment. Performing similarly well as the underactuated thrusters system was the solar-sails-controlled spacecraft formation using a bang-bang controller. This shows that solar sails could be a viable propellantless technique for relative control. A linear control technique was able to bound errors to within a couple of hundred metres, using a hybrid propulsion system. Of the cases studied, only the fully-actuated thrusters-based system was able to explicitly track a circular trajectory, but had [Delta]V requirement of more than 100 times greater than that needed for tracking the natural, elliptical trajectory.

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Section: Dynamics Stability and Periodic Orbitsmentioning

confidence: 84%

Formation-Keeping Strategies At The Earth-Moon L4 Triangular Libration Point

Wong¹

2021

Preprint

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“…1960 onward Digital computers were used for numerical calculations and analysis which generated 3-D periodic orbits [15]- [24]. Halo and quasi Halo orbits were discovered [25] [26] [27] [28].…”

Section: General Three-body Problem (Tbp) and Its Current Statusmentioning

confidence: 99%

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Sharma

2024

IJAA

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“…We study the restricted fourbody problem as equal masses located at the vertices of an equilateral triangle which investigated the equilibrium points, zero velocity curves, and families of periodic orbits were studied by [9-10-11-12]. The stability, periodic orbits around the triangular points of the Earth-Moon system, (which is perturbed by the Sun), and calculation of a periodic solution for the Sun-Earth-Moon system using numerical integration is proved by [13][14]. The numerical technique of Poincare surface sections is used to generate periodic and quasiperiodic orbits [15,16].…”

Section: Introductionmentioning

confidence: 99%

Stability About Libration Points for Restricted Four-Body Problem

Ismail

Ibrahim

Zaghrout

et al. 2019

Al-Azhar Bulletin of Science

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In this work, the Restricted Four-Body Problem is formulated in Hamiltonian form. The canonical form for the system is obtained which represents the equations of motion. The collinear libration points are obtained, we have five collinear libration points. The non-collinear libration points are found which are three non collinear libration points, they are obtained for different angles between the sight of Sun and the plane of Earth-Moon. The periodic orbits around each of these libration points are studied using two methods. The first method depends on the reduction of order of differential equations and the second method depends on the Eigen values of the characteristic equation. Two codes of MATHEMATICA are constructed to apply these two methods on the Sun-Earth-Moon-Spacecraft. The Poincare sections are obtained using the first method, these sections are used to illustrate the intersect points of the trajectories with the plane perpendicular to the plane of motion about each of the collinear libration points. Mirror symmetry is explored about each of these points. The Lyapunov orbits, and the Lissajous orbits about each of the collinear libration points are the results obtained by the second method. The eccentricities and the periods of each orbit are obtained. This study illustrates that the motion about the libration point L2 is more stable than the motion about any other collinear libration points.

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Stable periodic orbits about the sun perturbed earth-moon triangularpoints.

Cited by 25 publications

References 3 publications

Formation-Keeping Strategies At The Earth-Moon L4 Triangular Libration Point

Formation-Keeping Strategies At The Earth-Moon L4 Triangular Libration Point

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Stability About Libration Points for Restricted Four-Body Problem

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