Resonance stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries

Resonance in the perturbations of a synchronous satellite due to angular rate of the earth-moon system around the sun and the earth’s rotation rate

“…By using the perturbation equations (4) and (5), we have expressed the equations of motion in the form of second order ordinary differential equations (13) and (14). From the solutions (15) and (16), it is seen that the denominators vanishes at the points where 13 1 k E   and 2 E   and the motion becomes indeterminate at these points. We applied a method given in Brown and Shook (1933) to study the motion at these resonance points.…”

“…To study the motion of satellite at the point where 13 1 k E   , we will follow the procedure as given in Brown and Shook [3]. It is proposed to find the solution of Equation (14) when that of the unperturbed equation…”

“…He applied a numerical method to the region of the main belt of asteroids showing the relevance of several mean motion resonances (MMR) with several planets. Narayan and Singh [13] studied the existence of resonance and linear stability of the triangular equilibrium points of the planar restricted three body problem considering the photo gravitational effect of both the primaries in circular and elliptic case. The paper organization is as follows: Equations of motion of synchronous satellite are described in Sect.…”

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

“…where N is defined as: (25) The Hamiltonian H defined in equation (7) is reduced to the following form by help of the transformation given by (23). …”

“…The ER3BP are studied by [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The present paper investigates the stability of the infinitesimal mass about the triangular equilibrium points in both resonance and non-resonance case satisfying…”