= Tangentially driven motion on an axisymmetric surface
{title2=$\dot\phi^2=\frac{g h'(r)}{r+2r_\phi^2/r-r_{\phi\phi}}$}
Neglecting vertical acceleration and the vertical driving-force component, the radial normal reaction is $-Mg h'(r)$. A drive parallel to the horizontal velocity cancels when the radial acceleration equation is combined with $r_\phi/r$ times the azimuthal equation. For a prescribed path $r(\phi)$ this gives the displayed speed constraint. It describes the projected approximation, not arbitrary trajectories with substantial vertical motion.
// Target: classical-mechanics.bigb
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