A numerical investigation of the one-dimensional Newtonian three-body problem

1991 ◽  
Vol 51 (4) ◽  
pp. 379-394 ◽  
Author(s):  
Seppo Mikkola ◽  
Jarmo Hietarinta
Keyword(s):  
Numerical Investigation ◽  
Body Problem ◽  
Three Body Problem ◽  
One Dimensional ◽  
The One ◽  
Three Body

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

PERIODIC ORBITS NEAR A HETEROCLINIC LOOP FORMED BY ONE-DIMENSIONAL ORBIT AND A TWO-DIMENSIONAL MANIFOLD: APPLICATION TO THE CHARGED COLLINEAR THREE-BODY PROBLEM

2007 ◽  
Vol 17 (06) ◽  
pp. 2175-2183
Author(s):  
JAUME LLIBRE ◽  
DANIEL PAŞCA
Keyword(s):  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Negative Energy ◽  
Dimensional Manifold ◽  
Three Body Problem ◽  
Heteroclinic Loop ◽  
One Dimensional ◽  
Three Body ◽  
Total Collision

This paper is devoted to the study of a type of differential systems which appear usually in the study of the Hamiltonian systems with two degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near to the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear three-body problem.

scholarly journals Phasing Maneuver Analysis from a Low Lunar Orbit to a Near Rectilinear Halo Orbit

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 70
Author(s):  
Giordana Bucchioni ◽  
Mario Innocenti
Keyword(s):  
Body Problem ◽  
Halo Orbit ◽  
Preliminary Design ◽  
Three Body Problem ◽  
Third Body ◽  
Differential Correction ◽  
Target Station ◽  
The Third ◽  
The One ◽  
Three Body

The paper describes the preliminary design of a phasing trajectory in a cislunar environment, where the third body perturbation is considered non-negligible. The working framework is the one proposed by the ESA’s Heracles mission in which a passive target station is in a Near Rectilinear Halo Orbit and an active vehicle must reach that orbit to start a rendezvous procedure. In this scenario the authors examine three different ways to design such phasing maneuver under the circular restricted three-body problem hypotheses: Lambert/differential correction, Hohmann/differential correction and optimization. The three approaches are compared in terms of ΔV consumption, accuracy and time of flight. The selected solution is also validated under the more accurate restricted elliptic three-body problem hypothesis.

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