Variation of parameters methods embedding the jacobi integral resulting from energy parameter selection

摘要

The variation of parameters method known as BG14 (Bond & Gottlieb 14 element methdo)~1,2,3 is exceedingly powerful. The Jacobi integral embedded in the method is derived assuming a constant angular velocity of the central body. The perturbed algorithm formulations contained in Ref. 1. Ref. 2, and Ref. 3, also assume that the angular velocity of the central planet is constant. The effort to extend the original BG14 formulation to include non-constant angular velocity led to the realization that a new andmuch simpler, constant energy, formulation of the differnetial equations was possible. Also, the stability provided by the sliding origin technique~3 is easily retained in the extended methods, along with the choice of an energy level parameter, lambda, which can be used to keep the right hand side of the differential equations small and therefore more easily integrated.