Properties of the Liapunov stability zones of the Lagrange triangle

Authors:
E. A. Grebenikov;D. Kozak-Skoworodkin;N. I. Zemtsova
Affiliations:
Dorodnicyn Computing Center of RAS, Moscow, Russia;University of Podlasie, Poland;Dorodnicyn Computing Center of RAS, Moscow, Russia
Venue:
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Year:
2007

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The Mathematica book (4th edition)

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Numerical study of stability domains of hamiltonian equation solutions

CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing

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Abstract

We derived the quantitative estimates for geometrical parameters of the stability domains of the Lagrange triangle in the restricted three-body problem. We have shown that these domains are plane ellipse-similar figures, extended along a tangent to a circle, on which the Lagrange triangular solutions are located. We have proposed the heuristic algorithm for finding the maximal sizes of the stability domains.