Lagrangian coherent structures in the planar elliptic restricted three-body problem

2009 ◽  
Vol 103 (3) ◽  
pp. 227-249 ◽  
Author(s):  
Evan S. Gawlik ◽  
Jerrold E. Marsden ◽  
Philip C. Du Toit ◽  
Stefano Campagnola
Keyword(s):  
Coherent Structures ◽  
Body Problem ◽  
Lagrangian Coherent Structures ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

Lagrangian coherent structures in the planar parabolic/hyperbolic restricted three-body problem

2020 ◽  
Vol 493 (2) ◽  
pp. 1574-1586
Author(s):  
Qingyu Qu ◽  
Mingpei Lin ◽  
Ming Xu
Keyword(s):  
Phase Space ◽  
Coherent Structures ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Lagrangian Coherent Structures ◽  
Time Dependent ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body ◽  
Capture Trajectories

ABSTRACT It is clarified that the parabolic/hyperbolic restricted three-body problem (PRTBP/HRTBP) can be adopted to provide a simple description of the dynamics of fly-by asteroids or the close encounters between different galaxies. For these reasons, PRTBP and HRTBP have been investigated for long intervals of time. However, they are quite different from the circular restricted three-body problem due to the time-dependent and non-periodic dynamics. The Lagrangian coherent structures (LCSs), as a useful tool to analyse the time-dependent dynamical system, could be applied to explain some mechanics of the PRTBP and HRTBP. In this paper, we verify the invariant manifolds on the boundary manifolds of PRTBP by analysing the LCSs in proper Poincaré sections, which shows that it works in such a non-periodic problem. One of the contributions is to investigate the LCSs in the complete phase space of PRTBP, and then some natural escape and capture trajectories from or to the two main bodies can be obtained in this way. Another contribution is to establish and study the dynamics of HRTBP and its boundary. The LCSs can be introduced into this system, reasonably, to work as the analogues of the invariant manifolds, and the similar natural escape and capture trajectories corresponding to the two main bodies can also be obtained in the complete phase space of HRTBP. As a typical technique applied to fluid, flows to identify transport barriers in the time-dependent system, the LCSs provide an effective way to determine the time-dependent analogues of invariant manifolds for the PRTBP/HRTBP.

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.

scholarly journals Dynamics of the parabolic restricted three-body problem

2015 ◽  
Vol 29 (1-3) ◽  
pp. 400-415 ◽  
Author(s):  
Esther Barrabés ◽  
Josep M. Cors ◽  
Mercè Ollé
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body
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