The paper classifies four potentials (inverse-square, oscillator, oscillator plus inverse-square, and Morse) whose Newtonian equations can be embedded in higher-dimensional geometries where the motion is that of a free particle.
Lie,Theorie der Transformationsgrupprn: Vol I, Chelsea, Ne w York (1970)
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Linearization of Newton's second law
The paper classifies four potentials (inverse-square, oscillator, oscillator plus inverse-square, and Morse) whose Newtonian equations can be embedded in higher-dimensional geometries where the motion is that of a free particle.