Abstract
We have found that the introduction of the time element into the Kustaanheimo-Stiefel (K-S) regularization changes the rate of error growth from quadratic to linear with respect to the physical time, even when a scaling is not applied. It also mostly wipes out the periodic error components in the case of unperturbed orbits, independently of the application of the scaling. Since the increase in computational time due to use of the time element is negligible, we recommend that it be employed in all numerical integrations using the K-S regularization.
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