About the stability of the libration points of a rotating triaxial ellipsoid in a degenerate case

1973 ◽  
Vol 8 (1) ◽  
pp. 75-84 ◽  
Author(s):  
S. G. Zhuravlev
Keyword(s):  
Degenerate Case ◽  
Libration Points ◽  
Triaxial Ellipsoid ◽  
The Stability

Stability of the libration points of a rotating triaxial ellipsoid

1972 ◽  
Vol 6 (3) ◽  
pp. 255-267 ◽  
Author(s):  
S. G. Zhuravlev
Keyword(s):  
Libration Points ◽  
Triaxial Ellipsoid

scholarly journals Dynamics of Satellites Around Asteroids in Presence of Solar Radiation Pressure

2015 ◽  
Vol 10 (S318) ◽  
pp. 259-264
Author(s):  
Xiaosheng Xin ◽  
Daniel J. Scheeres ◽  
Xiyun Hou ◽  
Lin Liu
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Solar Radiation Pressure ◽  
Approximate Solutions ◽  
Triaxial Ellipsoid ◽  
Stability Maps ◽  
The Stability ◽  
Near Earth Asteroids

AbstractDue to the close distance to the Sun, solar radiation pressure (SRP) plays an important role in the dynamics of satellites around near-Earth asteroids (NEAs). In this paper, we focus on the equilibrium points of a satellite orbiting around an asteroid in presence of SRP in the asteroid rotating frame. The asteroid is modelled as a uniformly rotating triaxial ellipsoid. When SRP comes into play, the equilibrium points transformed into periodic orbits termed as``dynamical substitutes". We obtain the analytical approximate solutions of the dynamical substitutes from the linearised equations of motion. The analytical solutions are then used as initial guesses and are numerically corrected to compute the accurate orbits of the dynamical substitutes. The stability of the dynamical substitutes is analysed and the stability maps are obtained by varying parameters of the ellipsoid model as well as the magnitude of SRP.

scholarly journals Effect of Perturbed Potentials on the Stability of Libration Points in the Restricted Problem

1979 ◽  
Vol 81 ◽  
pp. 57-57
Author(s):  
K. B. Bhatnagar ◽  
P. P. Hallan
Keyword(s):  
Restricted Problem ◽  
Classical Problem ◽  
Oblate Spheroid ◽  
Libration Points ◽  
The Other ◽  
Triangular Points ◽  
Oblate Spheroids ◽  
The Stability

The location and the stability of the libration points in the restricted problem have been studied when there are perturbations in the potentials between the bodies. It is seen that if the perturbing functions involving the parameters α,α1,α2 satisfy certain conditions, there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable and for the triangular points, the range of stability increases or decreases depending upon whether the perturbation point (α,α1,α2) lies on one or the other side of the plane Aα + Bα1 + Cα2 = 0, and it remains the same if the point lies on the plane, where A,B,C depend on the perturbations. The theory is verified in the following four cases: (1) there are no perturbations in the potentials (classical problem), (2) only the bigger primary is an oblate spheroid, (3) both the primaries are oblate spheroids, and (4) the primaries are spherical in shape and the bigger is a source of radiation.

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