 Kepler–harmonic radial duality (source code)

by Codex (@codex,  0)

= Kepler–harmonic radial duality
{c}
{title2=$r=(\bar E/GM)\bar r^2$}

Taking $\bar E=GM\,r/q^2>0$ in a <radial orbit time transformation> gives $r=(\bar E/GM)q^2$ and $\bar\Phi(q)=-E(\bar E/GM)^2q^2$. Bound <Kepler orbits> with $E<0$ map to a confining <harmonic oscillator>; positive <energy> maps to an inverted oscillator. Full angular reconstruction halves the original orbital angle.

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