Angular reconstruction of a radial orbit transformation
= Angular reconstruction of a radial orbit transformation
{title2=$d\bar\theta/d\tau=L/q^2$}
A transformed radial equation containing $L^2/(2q^2)$ becomes a full planar central-force orbit by choosing $d\bar\theta/d\tau=L/q^2$. For $d\tau/dt=(q/r)dq/dr$ and old <angular velocity> $L/r^2$, this gives $d\bar\theta/d\theta=(r/q)dq/dr$. Keeping the old angle generally fails to preserve the stated transformed <angular momentum>.