Full paper in PDF:
$%A. Deprit and T. López Moratalla, Estabilidad orbital de satélites estacionarios, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2, 311–333.%$

Estabilidad orbital de satélites estacionarios
André DEPRIT and Teodoro LÓPEZ MORATALLA
Nationa Institute of Standards and Technology

Gaithersburg, MD 20899 -- USA

andre.deprit@nist.gov
Real Instituto y Observatorio de la Armada

11110 San Fernando -- Spain

ccgeneral@czvl.uca.es

Received: May 31, 1995
 
ABSTRACT

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.

1991 Mathematics Subject Classification: 68q40, 70-04, 70F15, 70H15, 70J25.