AAS 99-202

Variation of Parameter Methods Embedding the Jacobi Integral Resulting from Energy Parameter Selection

R.G. Gottlieb

The Boeing Company


Several different variation of parameters methods that inherit from Burdet's method and that embed the Jacobi integral are derived. Slight variations in the energy parameter construction result in variational equations that are equivalent but different in form. The parameters and formulation of the methods are universal and hence applicable to any type orbit. The Jacobi integral embedded in this method was derived assuming constant angular velocity for the central body. The perturbed algorithm formulations presented place no restriction on the central body velocity. A simple method of removing an instability that appears in the Burdet and KS (and perhaps other) methods for certain classes of problems is presented. This approach is used to build a piece-wise constant energy method. A number of test cases are included that illustrate the accuracy of the methods.