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Abstract
In this paper, restricted, three-body problem (RTBP) is generalised to study the non-linear stability of equilibrium points in the photogravitational RTBP with P-R drag. In the present study, both primaries are considered as a source of radiation and effect of P-R drag. Hence the problem will contain four parameters q1, q2, W1 and W2. At first, the Lagrangian and the Hamiltonian of the problem were computed, then the Lagrangian function is expanded in power series of the coordinates of the triangular equilibrium points x and y. Lastly, diagonalized the quadratic term of the Hamiltonian of the problem, which is obtained by expanding original Lagrangian or Hamiltonian by Taylor's series about triangular equilibrium point. Finally, the study concluded that the diagonalizable Hamiltonian is H2=ω1I1-ω2I2.
Highlights
Poynting [8] investigated the effect of radiation pressure on the moving particle in Interplanetary space and stated that the particle such as meteors or cosmic dust are comparably affected by gravitational and light radiation pressure force as they approach uminous Celestial bodies
The Lagrangian and the Hamiltonian of the problem were computed, the Lagrangian function is expanded in power series of the coordinates of the triangular equilibrium points x and y
Singh and Ishwar [12] examined the stability of triangular points in the generalised photogravitational RTBP by considering both primaries as oblate spheroid and shown that triangular points are stable
Summary
Poynting [8] investigated the effect of radiation pressure on the moving particle in Interplanetary space and stated that the particle such as meteors or cosmic dust are comparably affected by gravitational and light radiation pressure force as they approach uminous Celestial bodies. Robertson [10] modified Poynting theory in keeping with the principle of relativity He considered only terms of first order in the ratio of velocity of the particle to that of light. Ragos and Zafiropoulos [9] studied the existence and stability of equilibrium points for particle moving in the vicinity of two massive bodies, which exerts light radiation pressure with P-R drag numerically and concludes that none of the equilibrium points is stable. Vivek Kumar Mishra et al [13] examined the stability of triangular equilibrium points in photogravitational elliptic RTBP with P-R drag. Vivek Kumar Mishra and Ishwar [14] examined the non-linear stability of triangular equilibrium points in the photogravitational elliptic RTBP with P-R drag. Using the method described in Jorba [5], diagonalization of the quadratic part of the Hamiltonian of the photogravitational RTBP with P-R drag is carried out
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