Linearization of the Hamiltonian in the generalized photogravitational Chermnykh’s problem

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The dynamical behaviour of near by trajectories is being estimated by Lyapunov Characteristic Exponents (LCEs) in the Generalized Photogravitational ChermnykhLike problem. It is found that the trajectories of the Lagrangian point L 4 move along the epicycloid path, and spirally depart from the vicinity of the point. The LCEs remain positive for all the cases and depend on the initial deviation vector as well as renormalization time step. It is noticed that the trajectories are chaotic in nature and the L 4 is asymptotically stable. The effects of radiation pressure, oblateness and mass of the belt are also examined in the present model.

Section: Trajectory Of Lmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trajectories of L 4 and Lyapunov Characteristic Exponents in the Generalized Photogravitational Chermnykh-Like problem

Kushvah

2011

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“…The coordinates of m 1 , m 2 are (−μ, 0), (1 − μ, 0) respectively. In the above mentioned reference system and Miyamoto and Nagai (1975) model, the equations of motion of the infinitesimal mass particle in the xy-plane formulated as (please see Kushvah 2008Kushvah , 2009a):…”

Section: Location Of the Lagrangian Pointsmentioning

confidence: 99%

Trajectory and stability of Lagrangian point L 2 in the Sun-Earth system

Kushvah

2010

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This paper describes design of the trajectory and analysis of the stability of collinear point L 2 in the SunEarth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the model for the Sun-Earth system. The effect of radiation pressure of the Sun and oblate shape of the Earth are considered. The point L 2 is asymptotically stable up to a specific value of time t correspond to each set of values of parameters and initial conditions. The results obtained from this study would be applicable to locate a satellite, a telescope or a space station around the point L 2 .

“…Indeed, the restricted three-body problem has been a useful model in many fields, such as the evolution of binary stars (Eggleton 1983) and orbital calculations of planetary systems (Mikkola et al 1994;Namouni 1999). Moreover, modifications of the restricted three-body problem were employed to model various problems related to planetary systems (Chermnykh 1987;Papadakis 2004Papadakis , 2005aPapadakis , 2005bPerdios, Kalantonis & Douskos 2008;Kushvah 2008aKushvah , 2008bKushvah , 2009Kushvah , 2011aKushvah , 2011bDouskos 2011;Kushvah, Kishor & Dolas 2012;Kishor & Kushvah 2013;Douskos et al 2012;Douskos 2015).…”

Section: Introductionmentioning

confidence: 99%

Galaxies with supermassive binary black holes: (III) The Roche Lobes and Jiang-Yeh Lobe in a core system

Yeh¹,

Jiang²

2016