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 ; 534-537
2011-11-26
4 pages
Article (Journal)
Electronic Resource
English
On equilibrium stability in the Sitnikov problem
Online Contents | 2011
|On Dumbbell Motions in the Generalized Circular Sitnikov Problem
Springer Verlag | 2024
|