工程基础力学 Ⅱ 动力学 课件 Chapter 1 Kinematics of a Particle、Chapter 2 Fundamental Kinematics of a Rigid Bod

Chapter1

KinematicsofaParticle§1.1Motionequationofaparticle§1.2

Velocityandaccelerationofaparticle

Maincontents1.1MotionequationofaparticleThreetypicalmotionequation(1)Motionequationusing

vector(2)Motionequationusingrectangularcoordinate1.1Motionequationofaparticle(3)MotionequationusingnaturalcoordinateThreetypicalmotionequationThecrankofellipticcompassescanrotatearoundfixedaxisO,theendAishingedwithBC；ThepointsBandCcanmovealongtheverticalslidingchutes,respectively.FindthetrajectoryequationofaarbitrarypointMonBC.KnownExample11.1MotionequationofaparticleSolution:Consideranarbitraryposition，thecoordinateofMcanbeexpressedasfollowing:Eliminate

intheaboveequations,thetrajectoryequationofMcanbeobtainedas:

1.1Motionequationofaparticle1.2Velocityandaccelerationofaparticle(1)DefinitionforvelocityandaccelerationofaparticleusingvectorDisplacement：Velocity：Acceleration：(2)Definitionforvelocityandaccelerationofaparticleontherectangularcoordinate(3)

ProjectionforvelocityandaccelerationofaparticleonthenaturalaxesTangentNormalplaneOsculatingplanePrincipalnormalSubnormal(a)Naturalcoordinatesystem1.2Velocityandaccelerationofaparticle(3)

Projectionforvelocityandaccelerationofaparticleonthenaturalaxes(b)Velocityofaparticle(c)AccelerationofaparticleThefirstcomponentrepresentsthechangerateofspeedmagnitudefortheparticle,notedas()TangentialaccelerationThesecondcomponentrepresentsthechangerateofspeeddirectionfortheparticle,notedas()Normalacceleration1.2Velocityandaccelerationofaparticle(3)

Projectionforvelocityandaccelerationofaparticleonthenaturalaxes◆Tangentialacceleration◆NormalaccelerationTangentialacceleration

representsthechangerateofspeedmagnitudetotime,itsalgebraicvalueisequaltothefirstderivativeofthealgebraicvalueofvelocitytotime,orthesecondderivativeofcurvilinearcoordinatetotime,itisalongthetangentoftrajectory.

1.2Velocityandaccelerationofaparticle(1)Thevectormethodisusedtodeduceformula；(2)Therectangularcoordinateandnaturalcoordinatemethodsareusedtocalculate：Theadvantageofnaturalcoordinatemethodistheclearphysicalmeaningandmoresimplethanrectangularcoordinatemethod.Thedisadvantageisthetrajectorymustbeknown,whichlimitstheapplicability.Theadvantageofrectangularcoordinatemethodisthewideapplicability(whichcanonlybeusedwhenthetrajectoryisunknown).Thedisadvantageismorecomplexthannaturalcoordinatemethod.SummaryBothofthetwomethodsareneedtosolvesomeproblems

TheEnd

Chapter2FundamentalKinematicsofaRigidBody§2.1Translationalmotionofarigidbody§2.2Rotationofarigidbodyaboutafixedaxis§2.3Velocityandaccelerationofapointin

arigidbodyrotatingaboutafixedaxis

Maincontents1.

DefinitionThedirectionofthelinelinkingarbitrarytwopointsintherigidbodyneverchangesduringitsmotion.2.1Translationalmotionofarigidbody2.

FeaturesDifferentiate:Allparticlesinarigidbodywithtranslationalmotionhavethesametrajectories.Arbitrarytwoparticlesinarigidbodywithtranslationalmotionhavethesamevelocitiesandaccelerationsinthesameinstant.Themotionregularitiesofalltheparticlesinarigidbodywithtranslationalmotionarecompletelysame,sothetranslationofarigidbodycanbesimplifiedtothemotionofaparticleinit.2.1TranslationalmotionofarigidbodyExamplesoftranslationalmotion

2.1Translationalmotionofarigidbody1.

DefinitionTherearetwofixedpointsduringthemovementofarigidbody,itiscalledtherotationaboutafixedaxis.Theaxisisafixedlinethroughthetwofixedpoints.2.2Rotationofarigidbodyaboutafixedaxis2.FeaturesThedistancesbetweeneverypointintherigidbodyandthefixedaxisremainconstants.Everypointintherigidbodywhichisnotonthisaxismovesalongacircularpathinaplaneperpendiculartothisfixedaxis.3.Equationofrotationφ

isanalgebraicquantity.Signdefinitionofφ:followsright-handrule.φ

isthemonotropiccontinuousfunctionoftimet,whentherigidbodyrotates.

2.2Rotationofarigidbodyaboutafixedaxis4.Angularvelocityandangularaccelerationω

isanalgebraicquantitySigndefinitionofω:followsright-handrule.Unit：(1)Angularvelocity:

Inordertodescribethespeedanddirectionoftherotationofarigidbody,theangularvelocityisdefinedas,2.2Rotationofarigidbodyaboutafixedaxis4.Angularvelocityandangularacceleration(2)Angularacceleration:

Inordertodescribethespeedofangularvelocitychangedwithtimeoftherotationofarigidbody，theangularaccelerationisdefinedas,α

isanalgebraicquantitySigndefinitionofα:followsright-handrule.Unit：Arigidbodyhasacceleratedrotationwhenαand

havethesamesigns,deceleratedrotationwhenα

and

haveoppositesigns.

=const,uniformrotation.

α

=const,rotationwithconstantangularacceleration.2.2Rotationofarigidbodyaboutafixedaxis2.3Velocityandaccelerationofapointinarigidbodyrotatingaboutafixedaxis1.Themotionequationdefinedbycurvilinearcoordinate

2.Velocityofapoint

Differentiatetheexpressionabovewithrespecttotimet,gives

∵,

,∴itcanbeobtainedas,Directionofvelocity:alongthetangentline,pointtotherotationdirection.3.AccelerationofapointNormalacceleration:Tangentia