Periodic solutions of the restricted problem that are analytic continuations of periodic solutions of Hill's problem for small ?>0

1983 ◽  
Vol 30 (2) ◽  
pp. 115-132 ◽  
Author(s):  
L. M. Perko
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Hill’S Problem ◽  
Hill's Problem

Three-dimensional periodic solutions around equilibrium points in Hill's problem

1985 ◽  
Vol 35 (3) ◽  
pp. 257-267 ◽  
Author(s):  
C. Zagouras ◽  
V. V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Hill’S Problem ◽  
Hill's Problem

scholarly journals Transversal ejection-collision orbits for the restricted problem and the Hill's problem with applications

1988 ◽  
Vol 74 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Ernesto A Lacomba ◽  
Jaume Llibre
Keyword(s):  
Restricted Problem ◽  
Hill’S Problem ◽  
Hill's Problem ◽  
Collision Orbits

Symmetric periodic solutions of the Hill’s problem. I

2013 ◽  
Vol 51 (4) ◽  
pp. 275-288 ◽  
Author(s):  
A. B. Batkhin
Keyword(s):  
Periodic Solutions ◽  
Hill’S Problem ◽  
Hill's Problem

Symmetric periodic solutions of the Hill’s problem. II

2013 ◽  
Vol 51 (6) ◽  
pp. 452-464 ◽  
Author(s):  
A. B. Batkhin
Keyword(s):  
Periodic Solutions ◽  
Hill’S Problem ◽  
Hill's Problem

Hierarchy of periodic solutions families of spatial Hill’s problem

2009 ◽  
Vol 43 (2) ◽  
pp. 178-183 ◽  
Author(s):  
A. B. Batkhin ◽  
N. V. Batkhina
Keyword(s):  
Periodic Solutions ◽  
Hill’S Problem ◽  
Hill's Problem

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

scholarly journals Periodic Orbits Close to That of the Moon in Hill's Problem

2018 ◽  
Vol 5 ◽  
Author(s):  
Giovanni B. Valsecchi
Keyword(s):  
Periodic Orbits ◽  
The Moon ◽  
Hill’S Problem ◽  
Hill's Problem
Sign in / Sign up

Export Citation Format

Share Document