Parabolic coordinate system showing curves of constant & sigma; and & tau; the horizontal and vertical axes are the x and y coordinates respectively.
2.
That proves useful in solving the Hamilton-Jacobi equation in parabolic coordinates for the inverse-square central force problem of mechanics; for further details, see the Laplace Runge Lenz vector article.
3.
Degenerate motion also signals that the Hamilton Jacobi equations are completely separable in more than one coordinate system; for example, the Kepler problem is completely separable in both spherical coordinates and parabolic coordinates.
4.
I could also imagine putting the "'Conservation "'and "'Parabolic coordinates "'sections into two appendices, but that would interrupt the flow slightly; also, that seems not to be customary at WP . Willow 14 : 09, 31 December 2006 ( UTC)
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