On the adelphic potentials compatible with a set of planar orbits

Details On the adelphic potentials compatible with a set of planar orbits On the adelphic potentials compatible with a set of planar orbits

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..60..421e&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 60, no. 4, p. 421-430

Astronomy and Astrophysics

Astronomy

Bernoulli Theorem, Dynamic Characteristics, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Planar Structures, Boundary Layer Stability, Dynamic Stability, Orbital Mechanics, Polar Coordinates

Scientific paper

Given a planar potential B = B(x,y), compatible with a monoparametric family of planar orbits f(x,y) = c, we face the problem of producing potentials A = A(x,y), adelphic to B(x,y), i.e. nontrivial potentials which have in common with B(x,y) the given set of orbits. We establish a linear, second order partial differential equation for a function P(x,y) and we prove that, to any definite positive solution of this equation, there corresponds a potential A(x,y) adelphic to B(x,y).

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