Аннотация:
A treatment is given of the spatial restricted elliptic problem of three bodies
interacting under Newtonian gravity. The problem depends on two parameters: the ratio
between the masses of the main attracting bodies and the eccentricity of their elliptic orbits.
The eccentricity is assumed to be small. Nonlinear equations of motion of the test mass near a
triangular libration point are analyzed. It is assumed that the parameters of the problem lie on
the curves of third-order resonances corresponding to the planar restricted problem. In addition
to these resonances (their number is equal to five), the spatial problem has a resonance that
takes place at any parameter values since the the frequency of small linear oscillations of the
test mass along the axis perpendicular to the plane of the orbit of the main bodies is equal
to the frequency of Keplerian motion of these bodies. In this paper, the normal form of the
Hamiltonian function of perturbed motion through fourth-degree terms relative to deviations
from the libration point is obtained. Explicit expressions for the coefficients of normal form up
to and including the second degree of eccentricity are found.
Список литературы