scholarly journals Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem

1989 ◽  
Vol 77 (1) ◽  
pp. 167-198 ◽  
Author(s):  
Antonio Giorgilli ◽  
Amadeo Delshams ◽  
Ernest Fontich ◽  
Luigi Galgani ◽  
Carles Simó
Keyword(s):  
Hamiltonian System ◽  
Equilibrium Point ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Elliptic Equilibrium ◽  
Effective Stability ◽  
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.

On the modified circular restricted three-body problem with variable mass

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Libration Point ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lyapunov Orbits ◽  
Homoclinic Connections ◽  
Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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