Engineering Basic Mechanics Ⅱ Dynamics 工程基础力学 Ⅱ 动力学 课件 Chapter 9 d’Alembert Principle and Virtual Displacement Principle.pptx

Chapter9d’AlembertPrincipleandVirtualDisplacementPrinciple

§9.4Constraint,virtualdisplacement,virtualwork§9.5Principleofvirtualdisplacement§9.1InertialForceandd’AlembertPrincipleofaParticle§9.2d’AlembertPrincipleofaSystemofParticles§9.3ReductionofaSystemofInertialForcesofaRigidBodyMainContents

Inthischapter,wewilldiscussd’Alembertprinciple,itprovidesageneralmethodtosolvethekineticproblemofaparticleandasystemofparticles,themethodisthatthemethodsofstaticsareappliedtosolvekineticsproblems,thuskineticproblemscanbetransformedformallytoanequivalentstaticproblems,theycanbesolvedbytheoremofequilibrium.Thusthismethodiscalledthekinetic-staticmethod.Applyingthekinetic-staticmethodwecandeterminethemotion,forexampleaccelerationangularacceleration;canalsodeterminetheforce.D’Alembert’sPrinciple

ApplyingNewtonsecondlaw,wehave§9.1Inertialforceandd’AlembertprincipleofaparticleAssumingmassofaparticleis,accelerateis,activeforceactingontheparticleis,constraintforceis,showninfigure.AboveequationistransposedandwrittenasMakingWehavehasthedimensionofforce,iscalledtheinertialforceofparticle：itsmagnitudeisequaltotheproductofmassandaccelerationofparticle，itsdirectioniscontrarytothedirectionofparticleacceleration.Theactiveforce,constraintforceandvirtualinertialforceactingontheparticlecomposedformallyequilibratedsystemofforces，thisisd’Alembertprincipleofaparticle.

OlθExamole9-1§9.1Inertialforceandd’AlembertprincipleofaparticleShowninfigure,aconicalpendulum.Aballofmassm=0.1kgtiesaropeoflengthl=0.3m,oneendoftheropetiestoafixedpointO,andtheanglewiththeleadstraightlineisθ=60o.Ifthesmallballmakeuniformcircularmotioninthehorizontalplane,determinethevelocityof