Normalization of Hamiltonian in the Generalized Photogravitational Restricted Three Body Problem with Poynting–Robertson Drag

Abstract

We have performed normalization of Hamiltonian in the generalized photogravitational restricted three body problem with Poynting-Robertson drag. In this problem we have taken bigger primary as source of radiation and smaller primary as an oblate spheroid. Wittaker method is used to transform the second order part of the Hamiltonian into the normal form.

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.…”

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

“…The photogravitational restricted three body problem arises from the classical problem when at least one of the interacting bodies exerts radiation pressure, for example, binary star systems(both primaries radiating). The photogravitational restricted three body problem under different aspects was studied by Radzievskii (1950), Chernikov (1970), ?, Schuerman (1980), Ishwar and Kushvah (2006), Kushvah Sharma and Ishwar (2007a) The Poynting-Robertson drag named after John Henry Poynting and Howard Percy Robertson, is a process by which solar radiation causes dust grains in a solar system to slowly spiral inward. Poynting (1903) considered the effect of the absorption and subsequent re-emission of sunlight by small isolated particles in the solar system.…”

Stability of triangular equilibrium points in the Photogravitational elliptic restricted three body problem with Poynting-Robertson drag

“…He found that triangular equilibrium points are unstable in his problem. When we put a = 1 and e = 0 in equation (27) and (28), triangular equilibrium points are similar as in Kushvah [4]. From figure 2, we find that x and y both are increasing function of q 1 and decreasing function of A 2 .…”

“…With a = 1, e = 0 and A 2 = 0 triangular equilibrium points are same as Schuerman [10]. Kushvah [4] studied same problem in circular case. He found that triangular equilibrium points are unstable in his problem.…”