scholarly journals Nonlinear Stability of the Triangular Libration Points for Radiating and Oblate Primaries in CR3BP in Nonresonance Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Resonance Frequency ◽  
Radiation Pressure ◽  
Nonlinear Stability ◽  
Equilibrium Points ◽  
Kam Theory ◽  
Boundary Region ◽  
Libration Points ◽  
Triangular Libration Points ◽  
Nonresonance Condition ◽  
The Stability

This paper investigates the existence of resonance and nonlinear stability of the triangular equilibrium points when both oblate primaries are luminous. The study is carried out near the resonance frequency, satisfying the conditionsω1=ω2,  ω1=2ω2, andω1=3ω2in circular cases by the application of Kolmogorov-Arnold-Moser (KAM) theory. The study is carried out for the various values of radiation pressure and oblateness parameters in general. It is noticed that the system experiences resonance atω1=2ω2,  ω1=3ω2for different values of radiation pressures and oblateness parameter. The caseω1=ω2corresponds to the boundary region of the stability for the system. It is found that, except for some values of the radiation pressure, and oblateness parameters and forμ≤μc=0.0385209, the triangular equilibrium points are stable.

Analysis on nonlinear stability of the triangular libration points for radiating and oblate primaries in ER3BP

2017 ◽  
Vol 5 (1) ◽  
pp. 50
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Resonance Frequency ◽  
Linear Stability ◽  
Radiation Pressure ◽  
Nonlinear Stability ◽  
Binary Systems ◽  
Equilibrium Points ◽  
Boundary Region ◽  
Resonance Case ◽  
Triangular Libration Points ◽  
The Stability

In this paper we study the non linear stability of the triangular librations points in ER3BP considering both the primaries as radiating and oblate. The study is carried out near the resonance frequency satisfying the conditions  in resonance as well as non resonance case. The study is conducted for various values of radiation pressure and oblateness parameters. It is observed that the case corresponds to the boundary region of the stability for the system Further, it is examined that the system experiences resonance at for different values of radiation pressures and oblateness parameter. In non resonance case, it is observed that the equilibrium points are stable. In resonance case, for and the triangular equilibrium points are unstable. In case, when for some values of radiation pressure and oblateness parameter, it is stable and for some it is unstable. The model is best suited to the binary systems (Achird, Luyten, α Cen AB, Kruger- 60, Xi- Bootis).

scholarly journals Higher order resonance stability of triangular libration points for radiating primaries in ER3BP

2015 ◽  
Vol 3 (1) ◽  
pp. 26
Author(s):  
Ashutosh Narayan ◽  
Nutan Singh
Keyword(s):  
Binary Systems ◽  
Equilibrium Points ◽  
Boundary Region ◽  
Kam Theorem ◽  
Mass Ratio ◽  
Practical Application ◽  
Triangular Libration Points ◽  
Circular Case ◽  
Transformation Of Variables ◽  
The Stability

<p>The main aim of this paper is to study the existence of resonance and stability of the triangular equilibrium points in the framework of ER3BP when both the attracting bodies are sources of radiation at w<sub>1</sub>=w<sub>2</sub>, w<sub>1</sub>=2w<sub>2</sub>, w<sub>1</sub>=3w<sub>2</sub> in both circular and elliptical cases .A practical application of this model could be seen in the case of binary systems ( Achird, Luyten, α Cen- AB, Kruger 60, Xi Bootis). The study is carried out both analytically and numerically by considering various values of radiation pressures and around binary systems .In both cases (CR3BP and ER3BP) it is found that w<sub>1</sub>=w<sub>2</sub> corresponds to the boundary region of the stability for the system, whereas the other two cases w<sub>1</sub>=2w<sub>2</sub>, w<sub>1</sub>=3w<sub>2</sub>  correspond to the resonant cases. In order to investigate the stability, the Hamiltonian is normalized up to the fourth order by using linear canonical transformation of variables. Then KAM theorem is applied to investigate the stability for different values of radiation pressures in general and around the binary systems in particular. Finally, simulation technique is applied to study the correlation between radiation pressures and mass ratio in circular case; mass ratio and eccentricity in elliptical case. It is found that all the binary systems considered are stable. Also, it is found that except for some values of the radiation pressure parameters and for m&lt;=m<sub>c</sub> =0.0385209 the triangular equilibrium points are stable.</p>

scholarly journals Non- linear stability of triangular librations points in circular restricted three body under radiating and oblate primaries in presence of resonance

2015 ◽  
Vol 3 (2) ◽  
pp. 58
Author(s):  
Ashutosh Narayan ◽  
Nutan Singh
Keyword(s):  
Radiation Pressure ◽  
Fourth Order ◽  
Nonlinear Stability ◽  
Binary Systems ◽  
Normal Forms ◽  
Boundary Region ◽  
Third Order ◽  
Order Resonance ◽  
The Stability ◽  
Three Body

<p>The nonlinear stability of the triangular librations points is studied in the presence resonance considering both the primaries as radiating and oblate. The study is carried out for various values of radiation pressure and oblateness parameter in general and binary systems in particular. It is found that the normal forms of the Hamiltonian contains both the resonance cases; ω<sub>1</sub>= 2ω<sub>2 </sub>and ω<sub>1</sub>= 3ω<sub>2</sub>. The case ω<sub>1</sub>= ω<sub>2</sub> corresponds to the boundary region of the stability for the system.It is investigated that for the motion is unstable for third order resonance but stable for fourth order resonance.</p>

scholarly journals Dynamics of Satellites Around Asteroids in Presence of Solar Radiation Pressure

2015 ◽  
Vol 10 (S318) ◽  
pp. 259-264
Author(s):  
Xiaosheng Xin ◽  
Daniel J. Scheeres ◽  
Xiyun Hou ◽  
Lin Liu
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Solar Radiation Pressure ◽  
Approximate Solutions ◽  
Triaxial Ellipsoid ◽  
Stability Maps ◽  
The Stability ◽  
Near Earth Asteroids

AbstractDue to the close distance to the Sun, solar radiation pressure (SRP) plays an important role in the dynamics of satellites around near-Earth asteroids (NEAs). In this paper, we focus on the equilibrium points of a satellite orbiting around an asteroid in presence of SRP in the asteroid rotating frame. The asteroid is modelled as a uniformly rotating triaxial ellipsoid. When SRP comes into play, the equilibrium points transformed into periodic orbits termed as``dynamical substitutes". We obtain the analytical approximate solutions of the dynamical substitutes from the linearised equations of motion. The analytical solutions are then used as initial guesses and are numerically corrected to compute the accurate orbits of the dynamical substitutes. The stability of the dynamical substitutes is analysed and the stability maps are obtained by varying parameters of the ellipsoid model as well as the magnitude of SRP.

scholarly journals Unveiling Perturbing Effects of P-R Drag on Motion around Triangular Lagrangian Points of the Photogravitational Restricted Problem of Three Oblate Bodies

2021 ◽  
pp. 10-31
Author(s):  
Tajudeen Oluwafemi Amuda ◽  
Oni Leke ◽  
Abdulrazaq Abdulraheem
Keyword(s):  
Radiation Pressure ◽  
Equilibrium Points ◽  
Three Body Problem ◽  
Small Perturbations ◽  
Lagrangian Points ◽  
Triangular Points ◽  
Oblate Spheroids ◽  
The Stability ◽  
Zero Velocity Surfaces ◽  
Three Body

The perturbing effects of the Poynting-Robertson drag on motion of an infinitesimal mass around triangular Lagrangian points of the circular restricted three-body problem under small perturbations in the Coriolis and centrifugal forces when the three bodies are oblate spheroids and the primaries are emitters of radiation pressure, is the focus of this paper. The equations governing the dynamical system have been derived and locations of triangular Lagrangian points are determined. It is seen that the locations are influenced by the perturbing forces of centrifugal perturbation and the oblateness, radiation pressure and, P-R drag of the primaries. Using the software Mathematica, numerical analysis are carried out to demonstrate how the dynamical elements: mass ratio, oblateness, radiation pressure, P-R drag and centrifugal perturbation influence the positions of triangular equilibrium points, zero velocity surfaces and the stability. Our investigation reveals that, though the radiation pressure, oblateness and centrifugal perturbation decrease region of stability when motion is stable, however, they are not the influential forces of instability but the P-R drag. In the region when motion around the triangular points are stable an inclusion of the P-R drag of the bigger primary even by an almost negligible value of 1.04548*10-9 overrides other effect and changes stability to instability. Hence, we conclude that the P-R drag is a strong perturbing force which changes stability to instability and motion around triangular Lagrangian points remain unstable in the presence of the P-R drag.

Sign in / Sign up

Export Citation Format

Share Document