Physics
Scientific paper
Jun 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..11..483s&link_type=abstract
Celestial Mechanics, vol. 11, June 1975, p. 483-515. In Russian.
Physics
Circular Orbits, Lagrangian Equilibrium Points, Motion Stability, Orbit Calculation, Three Body Problem, Calculus Of Variations, Celestial Mechanics, Collinearity, Equations Of Motion, Libration, Orbit Perturbation, Roots Of Equations
Scientific paper
The problem of stability of three-dimensional periodic orbits near a collinear libration point is solved in the framework of the three-dimensional circular restricted three-body problem. Special attention is given to the study of the orbital stability of the examined periodic motions since, in the proper sense, all of these are unstable according to Liapunov. It is shown that it is sufficient to consider the equations in their variational form to solve the problem of stability. The orbital stability of the two- and three-dimensional solutions is proven by analysis of the roots of the corresponding characteristic equations, and the possibility of conditional stability in the linear approximation is demonstrated.
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