Linking low- to high-energy dynamics of invariant manifolds, transit orbits, and singular collision orbits in the planar circular restricted three-body problem

2019 ◽  
Vol 131 (11) ◽  
Author(s):  
Kenta Oshima
Keyword(s):  
Body Problem ◽  
Invariant Manifolds ◽  
High Energy ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Energy Dynamics ◽  
Three Body ◽  
Collision Orbits

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 Connecting orbits and invariant manifolds in the spatial restricted three-body problem

Nonlinearity ◽  
2004 ◽  
Vol 17 (5) ◽  
pp. 1571-1606 ◽  
Author(s):  
G Gómez ◽  
W S Koon ◽  
M W Lo ◽  
J E Marsden ◽  
J Masdemont ◽  
...  
Keyword(s):  
Body Problem ◽  
Invariant Manifolds ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Connecting Orbits ◽  
Three Body

scholarly journals A note on the existence of invariant punctured tori in the planar circular restricted three-body problem

1988 ◽  
Vol 8 (8) ◽  
pp. 63-72 ◽  
Keyword(s):  
Body Problem ◽  
Small Mass ◽  
Connected Components ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Jacobi Constant ◽  
Hill Region ◽  
The Masses ◽  
Three Body ◽  
Collision Orbits

AbstractThe existence of transversal ejection—collision orbits in the restricted three-body problem is shown to imply, via the KAM theorem, the existence, for certain intervals of (large) values of the Jacobi constant, of an uncountable number of invariant punctured tori in the corresponding (non-compact) energy surface. The proof is based on a comparison between Levi-Civita and McGehee regularizing variables. That these transversal ejection-collision orbits do actually exist was proved in [5] in the case where one of the primaries has a small mass and the zero-mass body revolves around the other (and for all values of the Jacobi constant compatible with the existence of three connected components for the Hill region); it is proved here without any restriction on the masses, well in the spirit of Conley's thesis [3].

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