Physics
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cosre..49..534k&link_type=abstract
Cosmic Research, Volume 49, Issue 6, pp.534-537
Physics
Scientific paper
The problem of stability of the trivial equilibrium position in the Sitnikov problem is considered in the first approximation. The first approximation is shown to have the form of a linear second-order equation with time-periodic coefficient (the Hill-type equation). The equilibrium stability was studied on the basis of equation regularization in the vicinity of a singular point with subsequent calculation of the trace a of the monodromy matrix. The equilibrium stability is shown to be stable for almost all values of eccentricity e from the [0, 1] interval. The instability takes place on the discrete set of e values, when the mutipliers are multiple (with non-simple elementary divisors), e = 1 being a point of crowding of this set.
Kalas V. O.
Krasil'Nikov P. S.
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