Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double-Averaging Can Fail to Characterize the Long-Term Evolution of
  Lidov-Kozai Cycles & Derivation of an Analytical Correction   The double-averaging (DA) approximation is widely employed as the standard
technique in studying the secular evolution of the hierarchical three-body
system. We show that effects stemmed from the short-timescale oscillations
ignored by DA can accumulate over long timescales and lead to significant
errors in the long-term evolution of the Lidov-Kozai cycles. In particular, the
conditions for having an orbital flip, where the inner orbit switches between
prograde and retrograde with respect to the outer orbit and the associated
extremely high eccentricities during the switch, can be modified significantly.
The failure of DA can arise for a relatively strong perturber where the mass of
the tertiary is considerable compared to the total mass of the inner binary.
This issue can be relevant for astrophysical systems such as stellar triples,
planets in stellar binaries, stellar-mass binaries orbiting massive black holes
and moons of the planets perturbed by the Sun. We derive analytical equations
for the short-term oscillations of the inner orbit to the leading order for all
inclinations, eccentricities and mass ratios. Under the test particle
approximation, we derive the "corrected double-averaging" (CDA) equations by
incorporating the effects of short-term oscillations into the DA. By comparing
to N-body integrations, we show that the CDA equations successfully correct
most of the errors of the long-term evolution under the DA approximation for a
large range of initial conditions. We provide an implementation of CDA that can
be directly added to codes employing DA equations.

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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc