Studies of Melnikov method and transversal homoclinic orbits in the circular planar restricted three-body problem

1996 ◽  
Vol 17 (12) ◽  
pp. 1177-1187 ◽  
Author(s):  
Zhu Ruzeng ◽  
Xiang Cheng
Keyword(s):  
Body Problem ◽  
Melnikov Method ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Transversal Homoclinic Orbits ◽  
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.

STABILIZATION OF CHAOTIC BEHAVIOR IN THE RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (10) ◽  
pp. 3603-3606 ◽  
Author(s):  
ARSEN DZHANOEV ◽  
ALEXANDER LOSKUTOV
Keyword(s):  
Body Problem ◽  
Chaotic Behavior ◽  
Melnikov Method ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lagrange Points ◽  
Three Body ◽  
Two Bodies

The restricted three-body problem on the example of a perturbed Sitnikov case is considered. On the basis of the Melnikov method we study a possibility to stabilize the obtained chaotic solutions by two bodies placed in the triangular Lagrange points. It is shown that in this case, in addition to regular and chaotic solutions, there exist stabilized solutions.

scholarly journals A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xuhua Cheng ◽  
Zhikun She
Keyword(s):  
Saddle Point ◽  
Chaotic Dynamics ◽  
Point Processes ◽  
Body Problem ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Smale Horseshoe ◽  
Birkhoff Theorem ◽  
Three Body

It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits. Since the standard Smale-Birkhoff theorem cannot be directly applied to indicate the chaotic dynamics of the Smale horseshoe type, we in this note alternatively apply the Conley-Moser conditions to analytically prove the existence of a Smale horseshoe in this classical restricted three-body problem.

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
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