Matrix perturbation methods using regularized coordinates

Details Matrix perturbation methods using regularized coordinates Matrix perturbation methods using regularized coordinates

Sep 1970

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1970cemec...2..311d&link_type=abstract

Celestial Mechanics, Volume 2, Issue 3, pp.311-318

Computer Science

Scientific paper

Matrix methods for computing perturbations of non-linear perturbed systems, as formulated by Alexeev, involve an expression for the full solution of the first variational equations of the system evaluated about a reference orbit. These cannot be immediately applied to a regularized system of equations where perturbations about Keplerian motion are considered since the solution of the variational equations of regularized Keplerian motion does not in general correspond to the solution of the variational equations of the unregularized equations. But, as Kustaanheimo and Stiefel have pointed out, the regularized equations of Keplerian motion should be excellent for the initiation of a perturbation theory since they are linear in form. This paper describes a method for applying Alexeev's theorem to a regularized system where full advantage is taken of the basic linear form of the unperturbed equations.

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