On the Stability of a Tethered System with a Free End in Elliptic Orbit

2001 ◽  
Vol 49 (2) ◽  
pp. 237-253
Author(s):  
M. Ruiz ◽  
J. Peláez ◽  
E. C. Lorenzini
Keyword(s):  
Elliptic Orbit ◽  
The Stability

On the stability of a satellite cylindrical precession in an elliptic orbit

1976 ◽  
Vol 40 (6) ◽  
pp. 984-991 ◽  
Author(s):  
A.P. Markeev ◽  
T.N. Chekhovskaia
Keyword(s):  
Elliptic Orbit ◽  
The Stability

scholarly journals On the stability of a resonant rotation of a satellite in an elliptic orbit

2016 ◽  
pp. 619-632 ◽  
Author(s):  
Б.С. Бардин ◽  
◽  
Е. Чекина ◽  
Keyword(s):  
Elliptic Orbit ◽  
The Stability

scholarly journals Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
José Laudelino de Menezes Neto ◽  
Gerson Cruz Araujo ◽  
Yocelyn Pérez Rothen ◽  
Claudio Vidal
Keyword(s):  
Stable Equilibrium ◽  
Center Of Mass ◽  
Radius Vector ◽  
Variable Length ◽  
Elliptic Orbit ◽  
Double Pendulum ◽  
Parametric Stability ◽  
Instability Regions ◽  
The Stability ◽  
Boundary Curves

<p style='text-indent:20px;'>We consider the planar double pendulum where its center of mass is attached in an elliptic orbit. We consider the case where the rods of the pendulum have variable length, varying according to the radius vector of the elliptic orbit. We make an Hamiltonian view of the problem, find four linearly stable equilibrium positions and construct the boundary curves of the stability/instability regions in the space of the parameters associated with the pendulum length and the eccentricity of the orbit.</p>

Attitude Stability of a Spinning Satellite in an Elliptic Orbit

1966 ◽  
Vol 33 (2) ◽  
pp. 402-405 ◽  
Author(s):  
T. R. Kane ◽  
P. M. Barba
Keyword(s):  
Symmetry Axis ◽  
Elliptic Orbit ◽  
Mass Center ◽  
Orbit Plane ◽  
Attitude Stability ◽  
The Stability

Floque´t theory is used to develop a procedure for testing the stability of a spinning, symmetric satellite whose mass center moves on an elliptic orbit while the symmetry axis remains normal to the orbit plane.

On the Stability of Planar Librations of a Dumb-bell Satellite in an Elliptic Orbit

1966 ◽  
Vol 70 (672) ◽  
pp. 1098-1102 ◽  
Author(s):  
R. C. Brereton ◽  
V. J. Modi
Keyword(s):  
Central Body ◽  
Stability Boundary ◽  
Elliptic Orbit ◽  
Gravity Gradient ◽  
Exact Equation ◽  
Local Gravity ◽  
Orbit Eccentricity ◽  
Librational Motion ◽  
The Stability

The planar librational motion of a dumb-bell satellite has been studied by several authors. In most cases the analysis has been restricted to circular or nearly circular orbits. In an elliptic orbit, the variation of the angular velocity of the satellite around the central body together with the change in the local gravity gradient provides the satellite with a mechanism for exchanging energy between the librational and orbital modes. In general, this imposes a limit on the orbit eccentricity for which stable (non-tumbling) librational motion is possible. This note investigates the bounds that must be placed on a disturbance applied to a slender gravity gradient stabilised satellite so that it will librate and not tumble. The determination of the stability boundary as presented here was arrived at by the numerical solution of the exact equation of motion, obtained using an IBM 7040 computer.

On the stability of a planar resonant rotation of a satellite in an elliptic orbit

2015 ◽  
Vol 20 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Boris S. Bardin ◽  
Evgeniya A. Chekina ◽  
Alexander M. Chekin
Keyword(s):  
Elliptic Orbit ◽  
The Stability

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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