scholarly journals Secular solutions at triangular equilibrium point in the generalized photogravitational restricted three body problem

2009 ◽  
Vol 323 (3) ◽  
pp. 317-317 ◽  
Author(s):  
B. Ishwar ◽  
A. Elipe
Keyword(s):  
Equilibrium Point ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Generalized Photogravitational ◽  
Three Body

scholarly journals Diagonalization of Hamiltonian in the photogravitation-al restricted three body problem with P-R drag

2017 ◽  
Vol 5 (2) ◽  
pp. 79 ◽  
Author(s):  
Xavier James Raj ◽  
Bhola Ishwar
Keyword(s):  
Power Series ◽  
Equilibrium Point ◽  
Body Problem ◽  
Equilibrium Points ◽  
Lagrangian Function ◽  
Quadratic Term ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body ◽  
Taylor’S Series

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.

scholarly journals Existence and Linear Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Oblateness

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jagadish Singh ◽  
Abubakar Umar Sandah
Keyword(s):  
Equilibrium Point ◽  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Second Primary ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Out Of Plane ◽  
Three Body

This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.

Sign in / Sign up

Export Citation Format

Share Document