Theorbitalmotionoftheouterfiveplanetsseemsrigorouslystableandquiteregularoverthistime-span(seealsoSection5).
3.2Time–frequencymaps
Althoughtheplanetarymotionexhibitsverylong-termstabilitydefinedasthenon-existenceofcloseencounterevents,thechaoticnatureofplanetarydynamicscanchangetheoscillatoryperiodandamplitudeofplanetaryorbitalmotiongraduallyoversuchlongtime-spans.Evensuchslightfluctuationsoforbitalvariationinthefrequencydomain,particularlyinthecaseofEarth,canpotentiallyhaveasignificanteffectonitssurfaceclimatesystemthroughsolarinsolationvariation(cf.Berger1988).
Togiveanoverviewofthelong-termchangeinperiodicityinplanetaryorbitalmotion,weperformedmanyfastFouriertransformations(FFTs)alongthetimeaxis,andsuperposedtheresultingperiodgramstodrawtwo-dimensionaltime–frequencymaps.Thespecificapproachtodrawingthesetime–frequencymapsinthispaperisverysimple–muchsimplerthanthewaveletanalysisorLaskar's(1990,1993)frequencyanalysis.
Dividethelow-passfilteredorbitaldataintomanyfragmentsofthesamelenh.Thelenhofeachdatasegmentshouldbeamultipleof2inordertoapplytheFFT.
Eachfragmentofthedatahasalargeoverlappingpart:forexample,whentheithdatabeginsfromt=tiandendsatt=ti+T,thenextdatasegmentrangesfromti+δT≤ti+δT+T,whereδT?T.WecontinuethisdivisionuntilwereachacertainnumberNbywhichtn+Treachesthetotalintegrationlenh.
WeapplyanFFTtoeachofthedatafragments,andobtainnfrequencydiagrams.
Ineachfrequencydiagramobtainedabove,thestrenhofperiodicitycanbereplacedbyagrey-scale(orcolour)chart.
Weperformthereplacement,andconnectallthegrey-scale(orcolour)chartsintoonegraphforeachintegration.Thehorizontalaxisofthesenewgraphsshouldbethetime,i.e.thestartingtimesofeachfragmentofdata(ti,wherei=1,…,n).Theverticalaxisrepresentstheperiod(orfrequency)oftheoscillationoforbitalelements.
WehaveadoptedanFFTbecauseofitsoverwhelmingspeed,sincetheamountofnumericaldatatobedecomposedintofrequencycomponentsisterriblyhuge(severaltensofGbytes).
这章没有结束^.^,请点击下一页继续阅读!
喜欢死在火星上请大家收藏:(m.easytpm.com)死在火星上阅文免费小说更新速度全网最快。