Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-Symmetrized Kustaanheimo-Stiefel Regularization   In this paper we describe a new algorithm for the long-term numerical
integration of the two-body problem, in which two particles interact under a
Newtonian gravitational potential. Although analytical solutions exist in the
unperturbed and weakly perturbed cases, numerical integration is necessary in
situations where the perturbation is relatively strong. Kustaanheimo--Stiefel
(KS) regularization is widely used to remove the singularity in the equations
of motion, making it possible to integrate orbits having very high
eccentricity. However, even with KS regularization, long-term integration is
difficult, simply because the required accuracy is usually very high. We
present a new time-integration algorithm which has no secular error in either
the binding energy or the eccentricity, while allowing variable stepsize. The
basic approach is to take a time-symmetric algorithm, then apply an implicit
criterion for the stepsize to ensure strict time reversibility. We describe the
algorithm in detail and present the results of numerical tests involving
long-term integration of binaries and hierarchical triples. In all cases
studied, we found no systematic error in either the energy or the angular
momentum. We also found that its calculation cost does not become higher than
those of existing algorithms. By contrast, the stabilization technique, which
has been widely used in the field of collisional stellar dynamics, conserves
energy very well but does not conserve angular momentum.

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio