Аннотация:
The well-known problem of the nonlinear stability of $L_4$ and $L_5$ in the circular spatial restricted three-body problem is revisited. Some new results in the light of the concept of Lie (formal) stability are presented. In particular, we provide stability and asymptotic estimates for three specific values of the mass ratio that remained uncovered. Moreover, in many cases we improve the estimates found in the literature.
Ключевые слова:restricted three-body problem, $L_4$ and $L_5$, elliptic equilibria, resonances, formal and Lie stability, exponential estimates.
Список литературы