3D homogeneous potentials producing isoenergetic families of orbits: An application to galactic dynamics. Issue 5 (22nd February 2022) - Kotoulas, Thomas
Abstract: In the light of the inverse problem of Newtonian dynamics, we study three‐dimensional homogeneous potentials V = V ( x, y, z ) of degree m producing a given two‐parametric family of regular orbits. Especially, we are interested in isoenergetic families of orbits, that is, families of orbits, which are described with constant energy ℰ = ℰ 0 by a test particle of unit mass. First, we offer the criteria, which must be fulfilled by the given family of regular orbits so that it can be created by such a potential. Second, we examine special cases, for example, ℰ 0 = 0, and we present families of orbits, which are generated by genuine 3D potentials. Finally, applications to galactic models are also given.