The Hamilton-Jacobi Theory

Abstract

AbstractAstronomers 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, $$ \begin{gathered} \ell = mean anomaly, L = \sqrt {\mu a} , \hfill \\ g = argument of the periapis, G = L\sqrt {1 - e^2 } , \hfill \\ h = longtitude of the node, H = G cos i, \hfill \\ \end{gathered} $$ (1.1) 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.KeywordsPoisson BracketHamiltonian FunctionCanonical TransformationJacobi EquationJacobi MappingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.