A study of non-collinear libration points in restricted three body problem with stokes drag effect when smaller primary is an oblate spheroid

Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of <i>L</i><sub>4</sub> in the Photogravitational Restricted Three Body Problem

“…The equations of motion of the infinitesimal mass 3 m in a synodic co-ordinate system ( , x y ) are 2 , 2 , ( ) 2 2 2 2 2 2 2 1 2 1 3 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 1 2 3 4 2 2 2 2 1 3 3 , 1 , , 1 2 4 4 2 2 , , ,  , we will reject second and higher order terms in 1 2 3 , , , p A A A and 4 A . We adopt the method used by Bhatnagar and Hallan [2] and give perturbation in Coriolis and centrifugal forces with the help of the parameters α and β respectively.…”

“…We use Moser's conditions by employing the iterative scheme of Henrard (Deprit and Deprit-Bartholome [1]), for transforming the involved Hamiltonian to the Birkhoff's normal form with the help of double D'Alembert's series. In the year 1983, Bhatnagar and Hallan [2] investigated the perturbation effects in Coriolis and centrifugal forces in the non-linear aspect of stability of 4 L . Rajiv Aggarwal et al [3] studied the non-linear stability of 4 L in the restricted three body problem for radiated axes symmetric primaries with resonances.…”

“…In the year 1983, Bhatnagar and Hallan [2] investigated the perturbation effects in Coriolis and centrifugal forces in the non-linear aspect of stability of 4 L . Rajiv Aggarwal et al [3] studied the non-linear stability of 4 L in the restricted three body problem for radiated axes symmetric primaries with resonances. Mamta Jain and Rajiv Aggarwal [4] investigated the existence of non-collinear libration points and their stability (in linear sense) in the circular restricted three body problem, in which they had considered the smaller primary as an oblate spheroid and the bigger one as a point mass including the effect of dissipative force especially Stokes drag.…”

“…Rajiv Aggarwal et al [3] studied the non-linear stability of 4 L in the restricted three body problem for radiated axes symmetric primaries with resonances. Mamta Jain and Rajiv Aggarwal [4] investigated the existence of non-collinear libration points and their stability (in linear sense) in the circular restricted three body problem, in which they had considered the smaller primary as an oblate spheroid and the bigger one as a point mass including the effect of dissipative force especially Stokes drag. Bhavneet Kaur and Rajiv Aggarwal [5] studied the Robe's restricted problem of 2 + 2 bodies when the bigger primary was a Roche ellipsoid.…”

“…We have extended this study by taking the primaries as axis symmetric bodies. In the present paper, our aim is to examine the effect of perturbations in Coriolis and centrifugul forces in the non-linear stability of the libration point 4 L of the restricted three body problem when both the primaries are axis symmetric bodies and the bigger primary is a source of radiation with its equatorial plane coincident with the plane of motion.…”