Families of periodic orbits in resonant reversible systems

2009 ◽  
Vol 40 (4) ◽  
pp. 511-537 ◽  
Author(s):  
Maurício Firmino Silva Lima ◽  
Marco Antonio Teixeira
Keyword(s):  
Periodic Orbits ◽  
Reversible Systems ◽  
Families Of Periodic Orbits

Families of Periodic Orbits for Solar Sails in the CRBTP

2014 ◽  
pp. 871-884 ◽  
Author(s):  
Patricia Verrier ◽  
Thomas Waters ◽  
Jan Sieber
Keyword(s):  
Periodic Orbits ◽  
Solar Sails ◽  
Families Of Periodic Orbits

Natural families of periodic orbits

1967 ◽  
Vol 72 ◽  
pp. 158 ◽  
Author(s):  
Andre Deprit ◽  
Jacques Henrard
Keyword(s):  
Periodic Orbits ◽  
Families Of Periodic Orbits ◽  
Natural Families

Bifurcations of Double Homoclinic Loops in Reversible Systems

2020 ◽  
Vol 30 (16) ◽  
pp. 2050246
Author(s):  
Yuzhen Bai ◽  
Xingbo Liu
Keyword(s):  
Coordinate System ◽  
Periodic Orbits ◽  
Homoclinic Orbit ◽  
Poincaré Map ◽  
Local Coordinate System ◽  
Reversible Systems ◽  
Bifurcation Equation ◽  
Bifurcation Phenomena ◽  
New Type ◽  
Symmetric Periodic Orbits

This paper is devoted to the study of bifurcation phenomena of double homoclinic loops in reversible systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equation, we perform a detailed study to obtain fruitful results, and demonstrate the existence of the R-symmetric large homoclinic orbit of new type near the primary double homoclinic loops, the existence of infinitely many R-symmetric periodic orbits accumulating onto the R-symmetric large homoclinic orbit, and the coexistence of R-symmetric large homoclinic orbit and the double homoclinic loops. The homoclinic bellow can also be found under suitable perturbation. The relevant bifurcation surfaces and the existence regions are located.

scholarly journals Stability of Periodic Planetary-Type Orbits of the General Planar N-Body Problem

1979 ◽  
Vol 81 ◽  
pp. 23-28
Author(s):  
John D. Hadjidemetriou
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Frame Of Reference ◽  
Rotating Frame ◽  
N Body Problem ◽  
Families Of Periodic Orbits ◽  
Special Case

It is known that families of periodic orbits in the general N-body problem (N≥3) exist, in a rotating frame of reference (Hadjidemetriou 1975, 1977). A special case of the above families of periodic orbits are the periodic orbits of the planetary type. In this latter case only one body, which we shall call sun, is the more massive one and the rest N-1 bodies, which we shall call planets, have small but not negligible masses. The aim of this paper is to study the properties of the families of periodic planetary-type orbits, with particular attention to stability. To make the presentation clearer, we shall start first with the case N=3 and we shall extend the results to N>3. We shall discuss planar orbits only.

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