Integrals of motion in the elliptic three-dimensional restricted three-body problem

1982 ◽  
Vol 26 (4) ◽  
pp. 353-360 ◽  
Author(s):  
E. Sarris
Keyword(s):  
Body Problem ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Integrals Of Motion ◽  
Three Body

scholarly journals Regular and Chaotic Motion in a Restricted Three–Body Problem of Astrophysical Interest

2000 ◽  
Vol 174 ◽  
pp. 281-285 ◽  
Author(s):  
J. C. Muzzio ◽  
F. C. Wachlin ◽  
D. D. Carpintero
Keyword(s):  
External Field ◽  
Body Problem ◽  
Stellar System ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stellar Orbits ◽  
System A ◽  
Regular And Chaotic Motion ◽  
Three Body

AbstractWe have studied the motion of massless particles (stars) bound to a stellar system (a galactic satellite) that moves on a circular orbit in an external field (a galaxy). A large percentage of the stellar orbits turned out to be chaotic, contrary to what happens in the usual restricted three–body problem of celestial mechanics where most of the orbits are regular. The discrepancy is probably due to three facts: 1) Our study is not limited to orbits on the main planes of symmetry, but considers three–dimensional motion; 2) The force exerted by the satellite goes to zero (rather than to infinity) at the center of the satellite; 3) The potential of the satellite is triaxial, rather than spherical.

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

BIFURCATIONS IN THE TOPOLOGY OF ZERO-VELOCITY SURFACES IN THE PHOTO-GRAVITATIONAL COPENHAGEN PROBLEM

2009 ◽  
Vol 19 (03) ◽  
pp. 1097-1111 ◽  
Author(s):  
T. J. KALVOURIDIS
Keyword(s):  
Body Problem ◽  
Small Body ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Radiation Sources ◽  
Trapping Regions ◽  
Zero Velocity Surfaces ◽  
Three Body

We study the evolution of the regions where three-dimensional motions of a small body are allowed in the Copenhagen case of the restricted three-body problem where one or both primaries, are radiation sources. We discuss the bifurcations in the topology of the zero-velocity surfaces, as well as in the trapping regions of the particle motion for various cases.

scholarly journals Approximate Analytical Three-Dimensional Multiple Time Scales Solution to a Circular Restricted Three-Body Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Fabao Gao ◽  
Yongqing Wang
Keyword(s):  
Time Scales ◽  
Body Problem ◽  
Three Dimensional ◽  
Classical Problem ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Chaotic Nature ◽  
Three Body

We illustrate the chaotic nature of the circular restricted three-body problem from the perspective of the bifurcation diagram with respect to the mass ratio parameter. Moreover, it is shown that when the frequency ratio in different directions of the classical problem is irrational, it has the quasiperiodic characteristics. In addition, a three-dimensional approximate solution to this problem under two time scales is proposed by using the multiple time scales method.

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