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

Stability of families of equatorial libration points of the gravitating and radiating triaxial ellipsoid

2010 ◽  
Author(s):  
S. G. Zhuravlev ◽  
Manuel de León ◽  
D. M. de Diego ◽  
R. M. Ros
Keyword(s):  
Libration Points ◽  
Triaxial Ellipsoid

scholarly journals PERIODIC ORBITS ASSOCIATED WITH THE LIBRATION POINTS OF THE HOMOGENEOUS ROTATING GRAVITATING TRIAXIAL ELLIPSOID

2012 ◽  
Vol 22 (10) ◽  
pp. 1230035 ◽  
Author(s):  
VOLODYMYR A. ROMANOV ◽  
EUSEBIUS J. DOEDEL
Keyword(s):  
Periodic Orbits ◽  
Boundary Value ◽  
Software Tool ◽  
Elliptical Galaxies ◽  
Libration Points ◽  
Numerical Continuation ◽  
Triaxial Ellipsoid ◽  
Computational Results ◽  
Small Bodies ◽  
Families Of Periodic Orbits

We present computational results for the families of periodic orbits that emanate from the five libration points of the homogeneous gravitating triaxial ellipsoid rotating around its small axis, as well as for various secondary bifurcating families. Possible applications of our results include research on the motion of stars and clusters in elliptical galaxies, and the design of space missions to the vicinity of small bodies (asteroids) and their libration points. The numerical continuation and bifurcation algorithms employed in our study are based on boundary value techniques, as implemented in the AUTO software tool.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

CURVATURE OF THE TRIAXIAL ELLIPSOID DEPENDING ON AZIMUTH ANGLE

2016 ◽  
Vol 72 (8) ◽  
Author(s):  
Sebahattin Bektas
Keyword(s):  
Azimuth Angle ◽  
Triaxial Ellipsoid

Stationkeeping controllers for Earth–Moon L1 and L2 libration points halo orbits

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Thiago César Lousada Marsola ◽  
Sandro da Silva Fernandes ◽  
José Manoel Balthazar
Keyword(s):  
Libration Points ◽  
Halo Orbits ◽  
L1 And L2
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