Given a planar potentialB=B(x, y), compatible with a monoparametric family of planar orbitsf(x, y)=c, we face the problem of producing potentialsA=A(x, y), adelphic toB(x, y), i.e. nontrivial potentials which have in common withB(x, y) the given set of orbits. We establish a linear, second order partial differential equation for a functionP(x, y) and we prove that, to any definite positive solution of this equation, there corresponds a potentialA(x, y) adelphic toB(x, y).
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Érdi, B., Bozis, G. On the adelphic potentials compatible with a set of planar orbits. Celestial Mech Dyn Astr 60, 421–430 (1994). https://doi.org/10.1007/BF00692026
- Inverse problem of Dynamics
- adelphic potentials