第76章 对火星轨道变化问题的最后解释(4/14)
termstabilityofsolarsystemplanetarymotion.forreaderswhohavemorespecificanddeeperinterestsinournumericalresults，wehavepreparedawebpage(access)，whereweshowraworbitalelements，theirlow-passfilteredresults，variationofdelaunayelementsandangularmomentumdeficit，andresultsofoursimpletime–frequencyanalysisonallofourintegrations.
insection2webrieflyexplainourdynamicalmodel，numericalmethodandinitialconditionsusedinourintegrations.section3isdevotedtoadescriptionofthequickresultsofthenumericalintegrations.verylong-termstabilityofsolarsystemplanetarymotionisapparentbothinplanetarypositionsandorbitalelements.aroughestimationofnumericalerrorsisalsogiven.section4goesontoadiscussionofthelongest-termvariationofplanetaryorbitsusingalow-passfilterandincludesadiscussionofangularmomentumdeficit.insection5，wepresentasetofnumericalintegrationsfortheouterfiveplanetsthatspans±5x1010yr.insection6wealsodiscussthelong-termstabilityoftheplanetarymotionanditspossiblecause.
2descriptionofthenumericalintegrations
（本部分涉及比较复杂的积分计算，作者君就不贴上来了，贴上来了起点也不一定能成功显示。）
2.3numericalmethod
weutilizeasecond-orderwisdom–holmansymplecticmapasourmainintegrationmethod(wisdomkinoshita，yoshidanakai1991)withaspecialstart-upproceduretoreducethetruncationerrorofanglevariables，‘warmstart’(sahatremaine1992，1994).
thestepsizeforthenumericalintegrationsis8dthroughoutallintegrationsofthenineplanets(n±1，2，3)，whichisabout111oftheorbitalperiodoftheinnermostplanet(mercury).asforthedeterminationofstepsize，wepartlyfollowthepreviousnumericalintegrationofallnineplanetsinsussmanwisdom(1988，7.2d)andsahatremaine(1994，22532d).weroundedthedecimalpartofthetheirstepsizesto8tomakethestepsizeamultipleof2inordertoreducetheaccumulationofround-offerrorinthecomputationprocesses.inrelationtothis，wisdomholman(1991)performednumericalintegrationsoftheouterfiveplanetaryorbitsusingthesymplecticmapwithastepsizeof400d，110.83oftheorbitalperiodofjupiter.theirresultseemstobeaccurateenough，whichpartlyjustifiesourmethodofdeterminingt
insection2webrieflyexplainourdynamicalmodel，numericalmethodandinitialconditionsusedinourintegrations.section3isdevotedtoadescriptionofthequickresultsofthenumericalintegrations.verylong-termstabilityofsolarsystemplanetarymotionisapparentbothinplanetarypositionsandorbitalelements.aroughestimationofnumericalerrorsisalsogiven.section4goesontoadiscussionofthelongest-termvariationofplanetaryorbitsusingalow-passfilterandincludesadiscussionofangularmomentumdeficit.insection5，wepresentasetofnumericalintegrationsfortheouterfiveplanetsthatspans±5x1010yr.insection6wealsodiscussthelong-termstabilityoftheplanetarymotionanditspossiblecause.
2descriptionofthenumericalintegrations
（本部分涉及比较复杂的积分计算，作者君就不贴上来了，贴上来了起点也不一定能成功显示。）
2.3numericalmethod
weutilizeasecond-orderwisdom–holmansymplecticmapasourmainintegrationmethod(wisdomkinoshita，yoshidanakai1991)withaspecialstart-upproceduretoreducethetruncationerrorofanglevariables，‘warmstart’(sahatremaine1992，1994).
thestepsizeforthenumericalintegrationsis8dthroughoutallintegrationsofthenineplanets(n±1，2，3)，whichisabout111oftheorbitalperiodoftheinnermostplanet(mercury).asforthedeterminationofstepsize，wepartlyfollowthepreviousnumericalintegrationofallnineplanetsinsussmanwisdom(1988，7.2d)andsahatremaine(1994，22532d).weroundedthedecimalpartofthetheirstepsizesto8tomakethestepsizeamultipleof2inordertoreducetheaccumulationofround-offerrorinthecomputationprocesses.inrelationtothis，wisdomholman(1991)performednumericalintegrationsoftheouterfiveplanetaryorbitsusingthesymplecticmapwithastepsizeof400d，110.83oftheorbitalperiodofjupiter.theirresultseemstobeaccurateenough，whichpartlyjustifiesourmethodofdeterminingt
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