Stabilization and Real World Satellite Problem
Many recent investigations have concerned themselves with the development of transformations which tend to “dynamically stabilize”, “regularize”, or otherwise “smooth” the classical Newtonian equations of unperturbed motion with the goal of improving the numerical behavior of the system for the perturbed case. Examples of such transformations include stabilization by the application of integrals, independent variable transformations, and dependent variable transformations for the case of highly perturbed motion. The specific transformations examined include the energy control term and element equations developed by Stiefel, Scheifele and Baumgarte, and time regularization techniques.
It is shown by computer simulations of several NASA satellite orbits that in many cases, while such transformations do tend to improve the error growth properties of the perturbed problem, they do so at an added expense which degrades the overall efficiency. It is further shown that this results from adverse effects these transformations have on (i) the numerical stability regions of the integrator, or (ii) local error uniformity, or (iii) formulation “overhead”. It is concluded that while such transformations may allow one to attain high precision results which are otherwise unattainable in classical formulations, with the exception of analytic stepsize control, they offer little or no advantage over the classical methods in the intermediate accuracy range, when overall efficiency is considered.
KeywordsControl Term Local Truncation Error True Anomaly Orbit Generator Time Regularize
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