Analysis of periodically time-varying systems

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1、J.A.RichardsAnalysisofPeriodicallyTime-VaryingSystemsWith73FiguresTechnischsHochschuleDarmstadtFachbereichMechanikBibliothek,_->lr(IMTISpringer-VerlagBerlinHeidelbergNewYork1983ContentsListofSymbolsPartITheoryandTechniques1Chapter1HistoricalPerspective31.1TheNa

2、tureofSystemswithPeriodicallyTime-VaryingParameters..31.21831-1887FaradaytoRayleigh-EarlyExperimentalistsandTheorists71.31918-1940TheFirstApplications91.4SecondGenerationApplications1011.5RecentTheoreticalDevelopments12;1.6CommonplaceIllustrationsofParametricBe

3、haviour12ReferencesforChapter114jProblems16Chapter2TheEquationsandTheirProperties172.1HillEquations172.2MatrixFormulationofHillEquations182.3TheStateTransitionMatrix192.4FloquetTheory202.5SecondOrderSystems222.6NaturalModesofSolution232.7ConcludingComments24Ref

4、erencesforChapter225Problems25Chapter3SolutionstoPeriodicDifferentialEquations273.1SolutionsOverOnePeriodoftheCoefficient273.2TheMeissnerEquation283.3SolutionatAnyTimeforaSecondOrderPeriodicEquation293.4Evaluationof4>(n,0)m,mIntegral303.5TheHillEquationwithaSta

5、ircaseCoefficient323.6TheHillEquationwithaSawtoothWaveformCoefficient323.6.1TheWronskianMatrixwithzNegative353.6.2TheWronskianMatrixwithzZero353.6.3TheCaseofßNegative363.7TheHillEquationwithaPositiveSlope,SawtoothWaveformCoefficient363.8TheHillEquationwithaTria

6、ngulärCoefficient37XContents3.9TheHillEquationwithaTrapezoidalCoefficient383.10BesselFunctionGeneration383.11TheHillEquationwithaRepetitiveExponentialCoefficient393.12TheHillEquationwithaCoefficientintheFormofaRepetitiveSequenceofImpulses403.13EquationsofHigher

7、Order413.14ResponsetoaSinusoidalForcingFunction413.15PhaseSpaceAnalysis443.16ConcludingComments46ReferencesforChapter348Problems49Chapter4Stability504.1TypesofStability504.2StabilityTheoremsforPeriodicSystems514.3SecondOrderSystems524.3.1StabilityandtheCharacte

8、risticExponent524.3.2TheMeissnerEquation534.3.3TheHillEquationwithanImpulsiveCoefficient564.3.4TheHillEquationwithaSawtoothWaveformCoefficient574.3.5TheHillEquationwithaTria