We show that L4 and L5 in the spatial restricted circular three-body problem are Nekhoroshev-stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev-stability of elliptic equilibria, namely to the case of "directional quasi-convexity", a notion introduced here, and to a (non-convex) steep case. We verify that the hypotheses are satisfied for L4 and L5 by means of numerically constructed Birkhoff normal forms.
Nekhoroshev-stability of L4 and L5 in the spatial restricted three--body problem
BENETTIN, GIANCARLO;FASSO', FRANCESCO;GUZZO, MASSIMILIANO
1998
Abstract
We show that L4 and L5 in the spatial restricted circular three-body problem are Nekhoroshev-stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev-stability of elliptic equilibria, namely to the case of "directional quasi-convexity", a notion introduced here, and to a (non-convex) steep case. We verify that the hypotheses are satisfied for L4 and L5 by means of numerically constructed Birkhoff normal forms.
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