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1. Chad A. Middleton, “ The 2D surfaces that generate Newtonian and general relativistic orbits with small eccentricities,” Am. J. Phys. 83(7), 608615 (2015).
2. Gary D. White, “ On trajectories of rolling marbles in cones and other funnels,” Am. J. Phys. 81(12), 890898 (2013) provides more information on the scalar case and how it differs from the full-blown vector version of the no-slip condition.
3. L. Q. English and A. Mareno, “ Trajectories of rolling marbles on various funnels,” Am. J. Phys. 80(11), 9961000 (2012). One might also compare to Eq. (24) of Ref. 2, which agrees with the English and Mareno result in the case of the scalar approximation.

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