For a satellite about an oblate planet in rotation about its axis of greatest inertia, conditions are given under which there may appear, in a frame fixed in the planet, two positions of equilibria with characteristic exponents that are purely imaginary. In which case, after appropriate normalization by Lie transformation executed mechanically through a symbolic algebraic processor, the theorem of Arnold about non definite quadratic forms is applied. It is concluded that the equilibria are stable in the sense of Liapunov. The conditions for stability are verified in the case of the earth.
@article{urn:eudml:doc:44232,
title = {Estabilidad orbital de sat\'elites estacionarios.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {9},
year = {1996},
pages = {312-333},
zbl = {0900.70376},
mrnumber = {MR1430781},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44232}
}
Deprit, André; López Moratalla, Teodoro. Estabilidad orbital de satélites estacionarios.. Revista Matemática de la Universidad Complutense de Madrid, Tome 9 (1996) pp. 312-333. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44232/