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1、EssentialMathandIntuitionforDealingwithaSecond-orderDynamicSystem–AprimerandreviewinanutshellforMEMSEngineersByChangLiu,MEMSCentral.comProfessorofEngineeringatNorthwesternUniversityOriginallycreatedNovember2,2010SecondrevisionMarch15,2011Disclaimer:Thetopicofdynamicsa
2、ndsecond-orderdynamicsystemistypicallycoveredinaquarterinmostschools–thisnoterepresentsahighlycondensedversion.Ibelieveitisimportanttocoveronlythemostindispensableandfrequentlyencounteredconcepts.Thesubjectofdynamicsystemsisdifficulttolearn,forthefollowingreasons:1.It
3、requiresgoodknowledgeofmathandgoodintuitiveunderstandingofphysics;2.Itinvolvesmanyconcepts,prettymessymath;3.Itistaughtfromeitherelectricalperspective,ormechanicalperspective,butrarelyboth.4.Manyteachersdon’treallyunderstanditthatwell.Thisreviewtriestocoverthetopicofs
4、ystemdynamicsinanaturalformat–fromtheperspectiveofalearner.Itisperfectforanundergraduateinengineeringoragraduatestudent.Thismanuscriptreviewsboththegeneralmethodologyandthemostcommoncases(understep-functionacceleration,undernaturalresponse,andundersinusoidalexcitation
5、).Aunifiedcoverageisimportantforstudentbodycoveringabroadspectrumofmajorsanddisciplines.Manystudentshavelearnedaboutdynamicsbefore.However,differentareas(EE,ME)havedifferentfocuses,differentterminologies,anduseddifferentnotations.Tomakethingsworse,manybookshavemademis
6、takesorhavenarrowfocusesthatdoesnotdiscussthebigpicture.Wehopethisnoteisuseful.1TableofContents:EssentialMathandIntuitionforDealingwithaSecond-orderDynamicSystem–AprimerandreviewinanutshellforMEMSEngineers.......................................................1I.Whati
7、sadynamicsystem?.........................................................................................3II.GeneralOverviewofSolutionstoDynamicSystems................................................4III.Differentialequationandcases....................................
8、.............................................5IV.Side-bar–BasicTrigonometry,ComplexNumber,andExponentialFunctionsandRelation
