Abstract
There is numerical evidence to support the conclusion that appropriate "matching" of the formulation of the equations of motion to the numerical integration method can lead to significant improvement in the accuracy and computational efficiency of the orbit generation process. This paper investigates this possibility from the point of view of matching a "Gaussian" variation of parameter (VOP) formulation with Adams type numerical integrators. The performance of the new orbit generators is then compared to the popular classical Cowell/Gauss-Jackson formulation/integrator pair.
Numerical results indicate that the VOP orbit generator can yield significant efficiency advantages. For example, after 28 days of integration of a synchronous orbit, a comparable accuracy (.5m) was attained with a VOP formulation at one-half the number of force model evaluations needed using the Cowell formulation.
It is suspected that the reasons one can do better with the VOP formulation include more favorable truncation error/stability region balancing. For example, it has been reported that lower order integration processes coupled with VOP are "better than" higher order processes. This supports the view that the VOP formulation results in a smaller stability region with the advantage of lower truncation error due to the more slowly varying parameters. An analytical approach to the study of this type of matching of the equation formulation to the numerical integration technique is given.
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References
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Velez, C.E., Cefola, P.J., Long, A.C., Nimitz, K.S. (1974). Calculation of precision satellite orbits with nonsingular elements (VOP formulation). In: Bettis, D.G. (eds) Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations. Lecture Notes in Mathematics, vol 362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066592
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DOI: https://doi.org/10.1007/BFb0066592
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