A Modified Hermite Integrator for Planetary Dynamics

Kokubo Eiichiro; Makino Junichiro

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A Modified Hermite Integrator for Planetary Dynamics

机译：改进的Hermite行星动力学积分器

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Wedescribeamodifiedtime-symmetricHermiteintegratorspecializedforthelong-termintegrationofplanetaryorbits.Ourtime-symmetricintegratorshavenosecularerrorsinthesemimajoraxisandtheeccentricityfortheintegrationoftwo-bodyKeplerproblemsasusualtime-symmetricandsymplecticintegrators.Theusualtime-symmetricorsymplecticintegrators,however,showaseculardriftintheargumentofpericenter.Ournewfamilyofintegratorshasonefreeparameter,whichwecanadjusttoreducetheerrorintheargumentofpericenterwithoutbreakingthetime-symmetryorchangingtheorderoftheintegrator.Weshowanalyticallythattheleadingtermoftheerrorvanishesforauniquevalueoftheparameter,whichisindependentofthesizeofthetimestepandtheeccentricity.Itisalsopossibletoeliminatethenon-leading,higher-ordertermsbyusingaparametervaluethatdependsonboththesizeofthetimestepandtheeccentricity.Wedescribethesecond-andthefourth-orderschemes.Anextensiontohigherorderisstraightforward.

机译：Wedescribeamodifiedtime-symmetricHermiteintegratorspecializedforthelong-termintegrationofplanetaryorbits.Ourtime-symmetricintegratorshavenosecularerrorsinthesemimajoraxisandtheeccentricityfortheintegrationoftwo-bodyKeplerproblemsasusualtime-symmetricandsymplecticintegrators.Theusualtime-symmetricorsymplecticintegrators，然而，showaseculardriftintheargumentofpericenter.Ournewfamilyofintegratorshasonefreeparameter，whichwecanadjusttoreducetheerrorintheargumentofpericenterwithoutbreakingthetime-symmetryorchangingtheorderoftheintegrator.Weshowanalyticallythattheleadingtermoftheerrorvanishesforauniquevalueoftheparameter，whichisindependentofthesizeofthetimestepandtheeccentricity.Itisalsopossibletoeliminatethenon领先，高ordertermsbyusingaparametervaluethatdependsonboththesizeofthetimestepandtheeccentricity.Wedescribethesecond-andthefourth-orderschemes.Anextensiontohigherorderisstraightforward。

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《PASJ: Publications of the Astronomical Society of Japan》 |2004年第5期|共页
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Kokubo Eiichiro; Makino Junichiro;
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A Modified Hermite Integrator for Planetary Dynamics

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