Nonlinear stability in the generalised photogravitational restricted three body problem with Poynting-Robertson drag

Abstract

The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.

Restricted Three Body Problem with Stokes Drag Effect

“…They have considered the smaller primary as an oblate body and bigger one as radiating and they have concluded that the triangular equilibrium points are unstable in linear sense. [16] has discussed the nonlinear stability in the generalized restricted three body problem with Poynting Robertson drag considering smaller primary as an oblate body and bigger one radiating. They have proved that the triangular points are stable in nonlinear sense.…”

Linear stability of equilibrium points in the generalized photogravitational Chermnykh’s problem

“…Ishwar and Kushvah (2006) examined the linear stability of triangular equilibrium points in the generalized photogravitational restricted three body problem with PoyntingRobertson drag, L 4 and L 5 points became unstable due to P-R drag which is very remarkable and important, where as they are linearly stable in classical problem when 0 < μ < μ Routh = 0.0385201. Kushvah et al (2007aKushvah et al ( , 2007bKushvah et al ( , 2007c examined normalization of Hamiltonian they have also studied the nonlinear stability of triangular equilibrium points in the generalized photogravitational restricted three body problem with Poynting-Robertson drag, they have found that the triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails. Papadakis and Kanavos (2007) given numerical exploration of the photogravitaional restricted five-body problem.…”

Restricted three-body problem with stokes drag effect when less massive primary is an ellipsoid

“…The effect of P-R drag on the existence and stability of libration points is dicussed by many authors as Chernikov [3]; Murray [20]; Kushvah et.al. [32]; Lhotka and Celletti [46]; Mishra et. al.…”