Qualitative Study of Motion Under the Potentials V/R=-AR/-A, ALPHA/E/R+

Details Qualitative Study of Motion Under the Potentials V/R=-AR/-A, ALPHA/E/R+ Qualitative Study of Motion Under the Potentials V/R=-AR/-A, ALPHA/E/R+

Mar 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..42..129c&link_type=abstract

Celestial Mechanics, Volume 42, Issue 1-4, pp. 129-139

Mathematics

Logic

Scientific paper

The two-parameter family of hamiltonians systems defined byH_{(a,α )} (r,θ ,p_r ,p_θ ) = (p_r^2 + p_θ ^2 r^{ - 2} )/2 - ar^{ - α } ,α ,a in Re ^ + is considerated. For every value of(a,α ) in Re ^ + × Re ^ + ,H_{(a,α )} is integrable, the energy H(a,α) and the angular momentum C(r,θ,pr,pθ)=pθ being two independent first integrals. Using appropriate coordinates, the natural foliation ofI h = ∪ c I hc is found-up to now, the sets Ih∩{c≥0} and Ih∩{c≤0} were studied separately and then their boundaries identified ([CLL], [D], [LL], for instance). As a corollary to this topological description, we obtain a relation between the value of the parametre α and the variation of the θ-coordinate along an orbit while it stays near collision or infinity.

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