Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem

1981 ◽  
Vol 23 (1) ◽  
pp. 97-106 ◽  
Author(s):  
I. A. Robin
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
Elliptic Restricted Problem

scholarly journals The Mechanism of Branching of Three-Dimensional Periodic Orbits from the Plane

1983 ◽  
Vol 74 ◽  
pp. 213-224
Author(s):  
I.A. Robin ◽  
V.V. Markellos
Keyword(s):  
Recent Work ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
General Situation ◽  
Orbital Symmetry ◽  
Resonant Orbits ◽  
Symmetry Properties ◽  
Elliptic Restricted Problem ◽  
Symmetric Periodic Orbits

AbstractA linearised treatment is presented of vertical bifurcations of symmetric periodic orbits(bifurcations of plane with three-dimensional orbits) in the circular restricted problem. Recent work on bifurcations from vertical-critical orbits (av = ±1) is extended to deal with the v more general situation of bifurcations from vertical self-resonant orbits (av = cos(2Πn/m) for integer m,n) and it is shown that in this more general case bifurcating families of three-dimensional orbits always occur in pairs, the orbital symmetry properties being governed by the evenness or oddness of the integer m. The applicability of the theory to the elliptic restricted problem is discussed.

scholarly journals Periodic orbits in the restricted problem of three bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Awadhesh Kumar Poddar ◽  
Divyanshi Sharma
Keyword(s):  
Perturbation Theory ◽  
Rigid Body ◽  
Coordinate System ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
General Perturbation ◽  
Triaxial Rigid Body ◽  
Three Dimensional Coordinate

AbstractIn this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.

Doubly symmetric periodic orbits in the three-dimensional restricted problem

1965 ◽  
Vol 70 ◽  
pp. 393 ◽  
Author(s):  
W. H. Jefferys
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
Symmetric Periodic Orbits

Some Periodic Orbits in the Elliptic Restricted Problem of Three Bodies

1970 ◽  
Vol 75 ◽  
pp. 315 ◽  
Author(s):  
Peter J. Shelus ◽  
Shiv S. Kumar
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Elliptic Restricted Problem

Existence of periodic orbits of the second kind in the elliptic restricted problem of three bodies

1975 ◽  
Vol 11 (1) ◽  
pp. 43-51 ◽  
Author(s):  
Anne Sergysels-Lamy
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Elliptic Restricted Problem

scholarly journals A Catalogue of Periodic Orbits in the Elliptic Restricted 3-Body Problem

1992 ◽  
Vol 152 ◽  
pp. 171-174 ◽  
Author(s):  
R. Dvorak ◽  
J. Kribbel
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Body Problem ◽  
Grid Size ◽  
Mass Ratios ◽  
Families Of Periodic Orbits ◽  
Elliptic Restricted Problem ◽  
The Stability

Results of families of periodic orbits in the elliptic restricted problem are shown for some specific resonances. They are calculated for all mass ratios 0 < μ < 1.0 of the primary bodies and for all values of the eccentricity of the orbit of the primaries e < 1.0. The grid size is of 0.01 for both parameters. The classification of the stability is undertaken according to the usual one and the results are compared with the extensive studies by Contopoulos (1986) in different galactical models.

scholarly journals ON THE BIFURCATION AND CONTINUATION OF PERIODIC ORBITS IN THE THREE BODY PROBLEM

2011 ◽  
Vol 21 (08) ◽  
pp. 2211-2219 ◽  
Author(s):  
K. I. ANTONIADOU ◽  
G. VOYATZIS ◽  
T. KOTOULAS
Keyword(s):  
Periodic Orbits ◽  
General Problem ◽  
Restricted Problem ◽  
Body Problem ◽  
Three Body Problem ◽  
Numerical Studies ◽  
Circular Problem ◽  
Families Of Periodic Orbits ◽  
Elliptic Restricted Problem ◽  
Three Body

We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only in particular resonances called "asymmetric resonances". However, numerical studies showed that in the general three body problem, asymmetric orbits may exist not only for asymmetric resonances, but for other kinds, too. In this work, we show the existence of asymmetric periodic orbits in the elliptic restricted problem. These families of periodic orbits continue existing and clarify the origin of many asymmetric periodic orbits in the general problem. Also, we illustrate how the families of periodic orbits of the restricted circular problem and those of the elliptic one join smoothly and form families in the general problem, verifying in this way the scenario first described by Bozis and Hadjidemetriou.

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