### Abstract

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).

Original language | English |
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Pages (from-to) | 421-430 |

Number of pages | 10 |

Journal | Celestial Mechanics & Dynamical Astronomy |

Volume | 60 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 1994 |

### Keywords

- Inverse problem of Dynamics
- adelphic potentials

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

Érdi, B., & Bozis, G. (1994). On the adelphic potentials compatible with a set of planar orbits.

*Celestial Mechanics & Dynamical Astronomy*,*60*(4), 421-430. https://doi.org/10.1007/BF00692026