Sur les solutions p�riodiques du mouvement plan de libration des satellites et des plan�tes

Abstract

R6surn6. Ce papier pr6sente une 6tude analytique du mouvement plan de rotation des satellites (et des plan6tes) dans leurs mouvements orbitaux. Les trois families des solution p6riodiques sont obtenues par la m6thode du prolongement analytique de Poincar6. Ensuite, la stabilit6 de ces solutions p6riodiques est discut6e, et les 6quations approch6es des courbes limites de stabilit6 sont donn6es jusqu'au quatri~me ordre.

Rotations of a near-symmetrical satellite in an elliptical orbit with Mercury-type resonance

“…3 They were subsequently studied in numerous papers. 4,[11][12][13] A thorough analysis of the function (2.7) was carried out 14,15 with emphasis on the behaviour of these functions at values of e close to unity.…”

“…Then, after substituting the values of the G k found into the right-hand side of equality (4.7) and performing some reduction taking notation (4.5) into account, we obtain the final expression for m (e): (4.11) Somewhat different forms of the analytical representation of the functions m (e) were previously obtained using Bessel functions. [13][14][15] …”