Possible conserved quantity for the Hénon-Heiles problem

Details Possible conserved quantity for the Hénon-Heiles problem Possible conserved quantity for the Hénon-Heiles problem

Aug 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phrva..42.1931f&link_type=abstract

Physical Review A (Atomic, Molecular, and Optical Physics), Volume 42, Issue 4, August 15, 1990, pp.1931-1945

Physics

8

Celestial Mechanics

Scientific paper

We study a power-series expansion for a conserved quantity K in the case of the two-dimensional Hénon-Heiles potential. An alternative technique to that of Gustavson [Astron. J. 71, 670 (1966)] is applied to find the coefficients in the expansion for K. The technique is used to determine twelve orders for the conserved quantity K, more than twice as many as that calculated by Gustavson. We investigate the degree of constancy of our truncated K in regions where the motion is known to be chaotic and also where it is nonchaotic.

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