The effect of Poynting–Robertson drag on the triangular Lagrangian points

In this study, we present a novel non-truncated strategy by accompanying the fixed-point iteration with traditional numerical integrators. The proposed non-truncated strategy aims to exactly integrate implicit motion equations that are directly derived from the Lagrangian of the post-Newtonian circular restricted three-body problem. In comparison with the commonly used truncated approach, which cannot exactly but approximately preserve the generalized Jacobian constant (or energy) of the original Lagrangian system, the proposed non-truncated strategy has been determined to preserve this constant well. In fact, the non-truncated strategy and the truncated approach have a difference at second post-Newtonian order. Based on Kolmogorov-Arnold-Moser theory, this difference from the truncation in the equations of motion may lead to destroying the orbital configuration, dynamical behavior of order and chaos, and conservation of the post-Newtonian circular restricted three-body problem. The non-truncated strategy proposed in this study can avoid all these drawbacks and provide highly reliable and accurate numerical solutions for the post-Newtonian Lagrangian dynamics. Finally, numerical results show that the non-truncated strategy can preserve the generalized Jacobian constant in the accuracy of O(10 −12 ), whereas the truncated approach at the first post-Newtonian (1PN) order only has an accuracy of O(10 −3 ). Moreover, several orbits are observed to be escaping from the bounded region in the 1PN truncated system via the truncated strategy, but these escaping orbits are unobserved via the non-truncated strategy.

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“….67 * 10 −11 × 1.9891 * which is coincident with the results in [6,41]. For other systems, the scaled parameter c will take different values.…”

Section: Dependence Of the Dynamics On Csupporting

confidence: 80%

Non-truncated strategy to exactly integrate the post-Newtonian Lagrangian circular restricted three-body problem

2018

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“…Then in our system of units the speed of light is equal to c = 22945.23619, for the case of Sun-Jupiter. 23,33 As can be noted, we have assumed that the post-Newtonian contribution to the angular velocity is too small, i.e ω = 1 + ω 1 /c 2 ≈ 1. In order to prove this assumption, let us start by considering that unlike the classical Newtonian system, the post-Newtonian angular velocity depends on the mass parameter µ and the speed of light c, i.e.…”

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confidence: 99%

Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system

Zotos

Dubeibe

2018

Int. J. Mod. Phys. D

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The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g., a comet, asteroid, meteor or spacecraft) in the planar Sun-Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index chaos indicator (SALI), we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with earlier ones, regarding other planetary systems.

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“…They found that the effect of perturbation factors are significant. In literature, many researchers have analyzed the photogravitational RTBP in nonlinear sense by considering one or two perturbations at a time (McKenzie and Szebehely 1981;Ishwar 1997;Subba Rao and Krishan Sharma 1997;Lhotka and Celletti 2015;Alvarez-Ramírez et al 2015) but very few of them have considered the problem under the combined influence of few perturbations (Kushvah et al 2007;Kishor and Kushvah 2017). Ishwar and Sharma (2012) have discussed about the nonlinear stability of out of plane equilibrium points in the RTBP with oblate primary and found that L 6 point is stable in nonlinear sense.…”

Section: Introductionmentioning

confidence: 99%

Normalization of Hamiltonian and Nonlinear Stability of Triangular Equilibrium Points in the Photogravitational Restricted Three Body Problem with P–R Drag in Non-resonance Case

Kishor

Raj

Ishwar

2019

Qual. Theory Dyn. Syst.

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Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical system in the vicinity of invariant objects. This paper presents the normalization of Hamiltonian and the analysis of nonlinear stability of triangular equilibrium points in non-resonance case, in the photogravitational restricted three body problem under the influence of radiation pressures and P-R drags of the radiating primaries. The Hamiltonian of the system is normalized up to fourth order through Lie transform method and then to apply the Arnold-Moser theorem, Birkhoff normal form of the Hamiltonian is computed followed by nonlinear stability of the equilibrium points is examined. Similar to the case of classical problem, we have found that in the presence of assumed perturbations, there always exists one value of mass parameter within the stability range at which the discriminant D 4 vanish, consequently, Arnold-Moser theorem fails, which infer that triangular equilibrium points are unstable in nonlinear sense within the stability range. Present analysis is limited up to linear effect of the perturbations, which will be helpful to study the more generalized problem.

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The effect of Poynting–Robertson drag on the triangular Lagrangian points

Cited by 35 publications

References 29 publications

Non-truncated strategy to exactly integrate the post-Newtonian Lagrangian circular restricted three-body problem

Non-truncated strategy to exactly integrate the post-Newtonian Lagrangian circular restricted three-body problem

Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system

Normalization of Hamiltonian and Nonlinear Stability of Triangular Equilibrium Points in the Photogravitational Restricted Three Body Problem with P–R Drag in Non-resonance Case

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