Abstract 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.
On equilibrium stability in the Sitnikov problem
Cosmic Research ; 49 , 6
2011
Article (Journal)
English
BKL: | 55.60 Raumfahrttechnik / 39.00 Astronomie: Allgemeines / 50.93 Weltraumforschung | |
Local classification TIB: | 770/3520/8000 |
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