第76章 对火星轨道变化问题的最后解释(8/14)
gorouslystableandquiteregularoverthistime-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).
atypicalexampleofthetime–frequencymapcreatedbytheaboveproceduresisshowninag
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).
atypicalexampleofthetime–frequencymapcreatedbytheaboveproceduresisshowninag
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