Real and Complex Potentials as Solutions to Planar Inverse Problem of Newtonian Dynamics by Thomas Kotoulas

“…If they are satisfied, such a potential exists and it is found analytically. For known families of curves, e.g., circles, parabolas, hyperbolas, etc., we find potentials that are compatible with them. …”
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Families of Planar Orbits in Polar Coordinates Compatible with Potentials by Thomas Kotoulas

“…If these conditions are fulfilled, then we can find a potential of the above form analytically. For the given families of curves, such as ellipses, parabolas, Bernoulli’s lemniscates, etc., we find potentials that produce them. …”
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Monoparametric Families of Orbits Produced by Planar Potentials by Thomas Kotoulas

“…Then, the potential function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>=</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></semantics></math></inline-formula> is found by quadratures. For known families of curves, e.g., ellipse, the logarithmic spiral, the lemniscate of Bernoulli, and circles, we find homogeneous and polynomial potentials that are compatible with this family of orbits. …”
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Regression Modeling for Spherical Data via Non-parametric and Least Square Methods by mosa golalizadeh, m moghimbeigy

“…They introduced two families of curves using differential geometry suitable for fitting the splines. …”
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