Periodic orbits for the perturbed planar circular restricted 3–body problem

Abouelmagd, Elbaz I.; Guirao, Juan Luis García; Llibre, Jaume

doi:10.3934/dcdsb.2019003

Cited by 20 publications

(19 citation statements)

References 43 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The classical restricted three-body problem with various perturbations has been studied by many researchers in the few decades. For example the existence as well as stability of the equilibrium points (e.g., Simmons et al (1985), Abouelmagd (2012), Abouelmagd and Abdullah (2019a), Selim et al (2019)), when the primaries are non spherical in shape (e.g., Sharma and Subba Rao (1979), Arredondo et al (2012)), the analysis of periodic orbits (e.g., Abouelmagd et al (2019b) ), the basins of convergence and classifications of orbits (e.g., Zotos (2015a), Zotos (2015b)) have been studied in restricted three-body problem.…”

Section: Introductionmentioning

confidence: 99%

On the spatial collinear restricted four-body problem with non-spherical primaries

Suraj¹,

Aggarwal²,

Mittal³

et al. 2020

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the third particle can orbit and the domain of basins of convergence linked to libration points in the spatial configuration of the collinear restricted four-body problem with non-spherical primaries (i.e., the primaries are oblate or prolate spheroid). The parametric evolution of the positions of the libration points as function of the oblateness and prolateness parameters of the primaries and the stability of these points in linear sense are illustrated numerically. Moreover, the numerical investigation shows that the only libration points which lie on either of the axes are linearly stable for several combinations of the oblateness parameter and mass parameter whereas the non-collinear libration points are found linearly unstable, consequently unstable in nonlinear sense also, for

show abstract

Section: Introductionmentioning

confidence: 99%

On the spatial collinear restricted four-body problem with non-spherical primaries

Suraj¹,

Aggarwal²,

Mittal³

et al. 2020

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

show abstract

“…The fundamental force governing this motion is mutual gravitational force between these bodies, "of course" this force is related to the gravitational potential between two bodies. In most cases, this force does not depend only on the mass and size of the bodies as well the separation distance between them, as stated in "Universal Newton's Law of Gravitation" but also on its shape, variation of mass, etc, which has a big significance in the dynamical behavior of body's motion, see for example, Abouelmagd et al (2019); Selim et al (2018); Suraj et al (2019). Although the word "universal" means that the law of gravitation can be applied at anywhere in the Universe, this law is valid only for two material particles (two points masses) where their masses are concentrated at the center of mass, not for bodies of finite dimensions or with arbitrary distribution of material mass.…”

Section: Introductionmentioning

confidence: 99%

Gravitational potential formulae between two bodies with finite dimensions

Ansari¹,

Abouelmagd

2020

Astron Nachr

View full text Add to dashboard Cite

The aim of this paper is to analyze and shed light on the potential relations between two bodies of finite dimensions and different shapes. After explaining the properties of different shaped bodies, we analyze the gravitational potential between an irregular body and a point mass, followed by the potential relation between two irregular bodies with discussion of its different properties. We also explore the potential relation between two solid cylinders, which can be degraded to 16 potential relations; one of these relations is the potential relation between two finite straight segments. With a new development for the potential relation, we evaluate the gravitational potential between a heterogeneous irregular body and a point mass followed by the potential between two heterogeneous irregular bodies with N−layers, which also can be reduced to the potential between two oblate or prolate heterogeneous bodies. We demonstrate that this relation can be degraded to many potential relations between two bodies, because it depends on the moments of inertia of the body's shape. Finally, we emphasize that this relation is considered a golden relation, which can be developed to generate the potential relation between different shaped bodies, either natural celestial bodies or between celestial and artificial bodies.

show abstract

“…They also used Lie transformation to eliminate the expressions, which involve inclination terms during the obtainment of required solutions. But the effect of non-sphericity and SRP are also studied within the framework of two and three bodies problem, for details see for instance [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Controlling the Perturbations of Solar Radiation Pressure on the Lorentz Spacecraft

et al. 2020

View full text Add to dashboard Cite

The aim of the present paper is to analyze the viability of using Lorentz Force (LF) acting on a charged spacecraft to neutralize the effects of Solar Radiation Pressure (SRP) on the longitude of the ascending node and the argument of perigee of the spacecraft’s orbit. In this setting, the Gauss planetary equations for LF and SRP are presented and averaged over the true anomaly. The averaged variations for the longitude of the ascending node (h) and the argument of perigee (g) are invariant under the symmetry (i,g)⟶(−i,−g) due to Lorentz Force. The sum of change rates due to both perturbing forces of LF and SRP is assigned by zero to estimate the charge amount to balance the variation for the argument of perigee and longitude of ascending. Numerical investigations have been developed to show the evolution of the charge quantity for different orbital parameters at both Low Earth and Geosynchronous Orbits.

show abstract

Periodic orbits for the perturbed planar circular restricted 3–body problem

Cited by 20 publications

References 43 publications

On the spatial collinear restricted four-body problem with non-spherical primaries

On the spatial collinear restricted four-body problem with non-spherical primaries

Gravitational potential formulae between two bodies with finite dimensions

Controlling the Perturbations of Solar Radiation Pressure on the Lorentz Spacecraft

Contact Info

Product

Resources

About