Boundary curves for families of planar orbits

Details Boundary curves for families of planar orbits Boundary curves for families of planar orbits

Apr 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..58..371b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 58, no. 4, p. 371-385

Mathematics

Dynamical Systems

19

Celestial Mechanics, Curves (Geometry), Orbit Calculation, Orbital Mechanics, Orbits, Boundaries, Dynamical Systems, Potential Fields

Scientific paper

For monoparametric families f(x,y) = c of planar orbits, created by a planar potential V(x,y), we introduce the notion of the family boundary curves (FBC). All members of the family f(x,y) = c are traced in an allowable region of the xy plane, defined by the corresponding FBC, with total energy E = E(c) varying along the family. Family boundary curves are also found for two-parametric families f(x,y,b) = c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potential V(x,y), to the FBC is studied.

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