The Hamilton-Jacobi Theory.

Astronomers in the nineteenth century found that the form of the Lagrange-Laplace equations for the perturbed Keplerian motion becomes very simple when the set of variables known as Delaunay variables, 1.1$$ \begin{gathered} \ell = mean anomaly, L = \sqrt {\mu a} , \hfill \\ g = argument of the periapis, G = L\sqrt {1 - e^2 } , \hfill \\ h = longtitude of the node, H = G cos i, \hfill \\ \end{gathered} $$ is used (see [15]). Here, μ is the product of the gravitational constant and the mass of the central body, a the semi-major axis, e the orbital eccentricity and i the inclination of the orbit over the reference plane. [ABSTRACT FROM AUTHOR]