Abstract
Given a two-parameter of three-dimensional orbits, we construct the unit tangent vector, the normal and the binormal which define the Frenet reference frame. In this frame, by writing that the force is conservative, we explicitly obtain the potential as a function of the energy along the trajectories and of its derivatives.
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Puel, F. Explicit solutions of the three-dimensional inverse problem of dynamics, using the frenet reference frame. Celestial Mech Dyn Astr 53, 207–218 (1992). https://doi.org/10.1007/BF00052609
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DOI: https://doi.org/10.1007/BF00052609