Classical Dynamics of Particles and Systems - 1st Edition

Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, ... 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HomePhysicalSciencesandEngineeringPhysicsandAstronomyBooksClassicalDynamicsofParticlesandSystemsBooksale:saveupto25%onindividualprintandeBookswithfreedelivery.UsepromocodeS&T25MoredetailsSelectcountry/regionUnitedStatesofAmericaUnitedKingdomAfghanistanÅlandIslandsAlbaniaAlgeriaAmericanSamoaAndorraAngolaAnguillaAntiguaandBarbudaArgentinaArmeniaArubaAustraliaAustriaAzerbaijanBahamasBahrainBangladeshBarbadosBelgiumBelizeBeninBermudaBhutanBoliviaBonaire,SintEustatiusandSabaBosniaandHerzegovinaBotswanaBrazilBritishIndianOceanTerritoryBritishVirginIslandsBruneiBulgariaBurkinaFasoBurundiCambodiaCameroonCanadaCanaryIslandsCapeVerdeCaymanIslandsCentralAfricanRepublicChadChileChinaChristmasIslandCocos(Keeling)IslandsColombiaComorosCongoCookIslandsCostaRicaCroatiaCubaCuraçaoCyprusCzechRepublicDemocraticRepublicoftheCongoDenmarkDjiboutiDominicaDominicanRepublicEcuadorEgyptElSalvadorEquatorialGuineaEritreaEstoniaEthiopiaFalklandIslands(Malvinas)FaroeIslandsFederatedStatesofMicronesiaFijiFinlandFranceFrenchGuianaFrenchPolynesiaGabonGambiaGeorgiaGermanyGhanaGibraltarGreeceGreenlandGrenadaGuadeloupeGuamGuatemalaGuernseyGuineaGuinea-BissauGuyanaHaitiHondurasHongKongHungaryIcelandIndiaIndonesiaIranIraqIrelandIsleofManIsraelItalyJamaicaJapanJerseyJordanKazakhstanKenyaKiribatiKuwaitKyrgyzstanLaoLatviaLesothoLiberiaLibyaLiechtensteinLuxembourgMacaoMacedoniaMadagascarMalawiMalaysiaMaldivesMaliMaltaMarshallIslandsMartiniqueMauritaniaMauritiusMayotteMexicoMoldovaMonacoMongoliaMontenegroMontserratMoroccoMozambiqueMyanmarNamibiaNepalNetherlandsNewCaledoniaNewZealandNicaraguaNigerNiueNorfolkIslandNorthKoreaNorthernMarianaIslandsNorwayOmanPakistanPalauPanamaPapuaNewGuineaParaguayPeruPhilippinesPitcairnPolandPortugalPuertoRicoQatarRéunionRomaniaRwandaSaintBarthélemySaintHelenaSaintKittsandNevisSaintLuciaSaintMartin(Frenchpart)SaintPierreandMiquelonSaintVincentandtheGrenadinesSamoaSanMarinoSaoTomeandPrincipeSaudiArabiaSenegalSerbiaSeychellesSierraLeoneSingaporeSintMaarten(Dutchpart)SlovakiaSloveniaSolomonIslandsSomaliaSouthAfricaSouthGeorgiaandtheSouthSandwichIslandsSouthKoreaSouthSudanSpainSriLankaSudanSurinameSvalbardandJanMayenSwazilandSwedenSwitzerlandSyriaTaiwanTajikistanTanzaniaThailandTimorLesteTogoTokelauTongaTrinidadandTobagoTunisiaTurkeyTurkmenistanTurksandCaicosIslandsTuvaluUgandaUkraineUnitedArabEmiratesUruguayUSVirginIslandsUzbekistanVanuatuVaticanCityVenezuelaVietnamWallisandFutunaWesternSaharaYemenZambiaZimbabwePurchaseoptionseBook$93.95DRM-free(PDF)DRM-FreeEasy-Downloadandstartreadingimmediately.There’snoactivationprocesstoaccesseBooks;alleBooksarefullysearchable,andenabledforcopying,pasting,andprinting.Flexible-Readonmultipleoperatingsystemsanddevices.EasilyreadeBooksonsmartphones,computers,oranyeBookreaders,includingKindle.Open-Buyonce,receiveanddownloadallavailableeBookformats,includingPDF,EPUB,andMobi(forKindle).eBookFormatHelpAddtocartSalestaxwillbecalculatedatcheck-outInstitutionalSubscriptionRequestaSalesQuoteRequestaSalesQuoteTaxExemptOrdersTaxExemptOrdersWecannotprocesstaxexemptordersonline.Ifyouwishtoplaceataxexemptorderpleasecontactus.SupportCenterReturns&RefundsFreeGlobalShippingNominimumorder50%offBookBundlesImmediatelydownloadyoureBookwhilewaitingforprintdelivery.Nopromocodeneeded.MoreDetailsDescriptionClassicalDynamicsofParticlesandSystemspresentsamodernandreasonablycompleteaccountoftheclassicalmechanicsofparticles,systemsofparticles,andrigidbodiesforphysicsstudentsattheadvancedundergraduatelevel.Thebookaimstopresentamoderntreatmentofclassicalmechanicalsystemsinsuchawaythatthetransitiontothequantumtheoryofphysicscanbemadewiththeleastpossibledifficulty;toacquaintthestudentwithnewmathematicaltechniquesandprovidesufficientpracticeinsolvingproblems;andtoimparttothestudentsomedegreeofsophisticationinhandlingboththeformalismofthetheoryandtheoperationaltechniqueofproblemsolving.Vectormethodsaredevelopedinthefirsttwochaptersandareusedthroughoutthebook.OtherchapterscoverthefundamentalsofNewtonianmechanics,thespecialtheoryofrelativity,gravitationalattractionandpotentials,oscillatorymotion,LagrangianandHamiltoniandynamics,central-forcemotion,two-particlecollisions,andthewaveequation.TableofContentsPrefaceChapter1.MatricesandVectors1.1Introduction1.2TheConceptofaScalar1.3CoordinateTransformations1.4PropertiesofRotationMatrices1.5MatrixOperations1.6FurtherDefinitions1.7GeometricalSignificanceofTransformationMatrices1.8DefinitionsofaScalarandaVectorinTermsofTransformationProperties1.9ElementaryScalarandVectorOperations1.10TheScalarProductofTwoVectors1.11TheVectorProductofTwoVectors1.12UnitVectorsSuggestedReferencesProblemsChapter2.VectorCalculus2.1Introduction2.2DifferentiationofaVectorwithRespecttoaScalar2.3ExamplesofDerivatives—VelocityandAcceleration2.4AngularVelocity2.5TheGradientOperator2.6TheDivergenceofaVector2.7TheCurlofaVector2.8SomeAdditionalDifferentialVectorRelations2.9IntegrationofVectorsSuggestedReferencesProblemsChapter3.FundamentalsofNewtonianMechanics3.1Introduction3.2Newton'sLaws3.3FramesofReference3.4TheEquationofMotionforaParticle3.5ConservationTheorems3.6ConservationTheoremsforaSystemofParticles3.7LimitationsofNewtonianMechanicsSuggestedReferencesProblemsChapter4.TheSpecialTheoryofRelativity4.1Introduction4.2GalileanInvariance4.3TheLorentzTransformation4.4MomentumandEnergyinRelativity4.5SomeConsequencesoftheLorentzTransformationSuggestedReferencesProblemsChapter5.GravitationalAttractionandPotentials5.1Introduction5.2TheGravitationalPotential5.3LinesofForceandEquipotentialSurfaces5.4TheGravitationalPotentialofaSphericalShell5.5AFinalCommentSuggestedReferencesProblemsChapter6.OscillatoryMotion6.1Introduction6.2TheSimpleHarmonicOscillator6.3DampedHarmonicMotion6.4ForcingFunctions6.5ForcedOscillations6.6PhaseDiagrams6.7TheResponseofLinearOscillatorstoImpulsiveForcingFunctions6.8ElectricalOscillations6.9HarmonicOscillationsinTwoDimensions6.10TheUseofComplexNotationSuggestedReferencesProblems7Chapter7.NonlinearOscillations7.1Oscillations7.2OscillationsforGeneralPotentialFunctions7.3PhaseDiagramsforNonlinearSystems7.4ThePlanePendulum7.5NonlinearOscillationsinaSymmetricPotential-TheMethodofSuccessiveApproximations7.6NonlinearOscillationsinanAsymmetricPotential-TheMethodofPerturbationsSuggestedReferencesProblemsChapter8.SomeMethodsintheCalculusofVariations8.1Introduction8.2StatementoftheProblem8.3Euler'sEquation8.4TheBrachistochroneProblem8.5The"SecondForm"ofEuler'sEquation8.6FunctionswithSeveralDependentVariables8.7TheEulerEquationsWhenAuxiliaryConditionsAreImposed8.8TheδNotationSuggestedReferencesProblemsChapter9.Hamilton'sPrinciple—LagrangianandHamiltonianDynamics9.1Introduction9.2Hamilton'sPrinciple9.3GeneralizedCoordinates9.4Lagrange'sEquationsofMotioninGeneralizedCoordinates9.5Lagrange'sEquationswithUndeterminedMultipliers9.6TheEquivalenceofLagrange'sandNewton'sEquations9.7TheEssenceofLagrangianDynamics9.8ATheoremConcerningtheKineticEnergy9.9TheConservationofEnergy9.10TheConservationofLinearMomentum9.11TheConservationofAngularMomentum9.12TheCanonicalEquationsofMotion—HamiltonianDynamics9.13SomeCommentsRegardingDynamicalVariablesandVariationalCalculationsinPhysics9.14PhaseSpaceandLiouville'sTheorem9.15TheVirialTheorem9.16TheLagrangianFunctioninSpecialRelativitySuggestedReferencesProblemsChapter10.Central-ForceMotion10.1Introduction10.2TheReducedMass10.3ConservationTheorems—FirstIntegralsoftheMotion10.4EquationsofMotion10.5OrbitsinaCentralField10.6CentrifugalEnergyandtheEffectivePotential10.7PlanetaryMotion-Kepler'sProblem10.8Kepler'sEquation10.9ApproximateSolutionofKepler'sEquation10.10ApsidalAnglesandPrecession10.11StabilityofCircularOrbits10.12TheProblemofThreeBodiesSuggestedReferencesProblemsChapter11.KinematicsofTwo-ParticleCollisions11.1Introduction11.2ElasticCollisions—Center-of-MassandLaboratoryCoordinateSystems11.3KinematicsofElasticCollisions11.4CrossSections11.5TheRutherfordScatteringFormula11.6TheTotalCrossSection11.7RelativisticKinematicsSuggestedReferencesProblemsChapter12.MotioninaNoninertialReferenceFrame12.1Introduction12.2RotatingCoordinateSystems12.3TheCoriolisForce12.4MotionRelativetotheEarthSuggestedReferencesProblemsChapter13.DynamicsofRigidBodies13.1Introduction13.2TheInertiaTensor13.3AngularMomentum13.4PrincipalAxesofInertia13.5MomentsofInertiaforDifferentBodyCoordinateSystems13.6FurtherPropertiesoftheInertiaTensor13.7TheEulerianAngles13.8Euler'sEquationsforaRigidBody13.9Force-FreeMotionofaSymmetricalTop13.10TheMotionofaSymmetricalTopwithOnePointFixed13.11TheStabilityofRigid-BodyRotationsSuggestedReferencesProblemsChapter14.SystemswithManyDegreesofFreedom—SmallOscillationsandNormalCoordinates14.1Introduction14.2TwoCoupledHarmonicOscillators14.3TheGeneralProblemofCoupledOscillations14.4TheOrthogonalityoftheEigenvectors14.5NormalCoordinates14.6TwoLinearlyCoupledPlanePendula14.7ThreeLinearlyCoupledPlanePendula—AnExampleofDegeneracy14.8TheLoadedString14.9TheContinuousStringasaLimitingCaseoftheLoadedString14.10TheWaveEquation14.11TheNonuniformString-OrthogonalFunctionsandPerturbationTheory14.12FourierAnalysisSuggestedReferencesProblemsChapter15.TheWaveEquationinOneDimension15.1Introduction15.2SeparationoftheWaveEquation15.3PhaseVelocity,Dispersion,andAttenuation15.4ElectricalAnalogies—FilteringNetworks15.5GroupVelocityandWavePackets15.6FourierIntegralRepresentationofWavePackets15.7EnergyPropagationintheLoadedString15.8FurtherCommentsRegardingPhaseandGroupVelocities15.9ReflectedandTransmittedWaves15.10DampedPlaneWavesSuggestedReferencesProblemsSolutions,Hints,andReferencesforSelectedProblemsAppendixA.Taylor'sTheoremExercisesAppendixB.ComplexNumbersB.1ComplexNumbersB.2GeometricalRepresentationofComplexNumbersB.3TrigonometricFunctionsofComplexVariablesB.4HyperbolicFunctionsExercisesAppendixC.OrdinaryDifferentialEquationsofSecondOrderC.1LinearHomogeneousEquationsC.2LinearInhomogeneousEquationsExercisesAppendixD.UsefulFormulasD.1BinomialExpansionD.2TrigonometricRelationsD.3TrigonometricSeriesD.4ExponentialandLogarithmicSeriesD.5HyperbolicFunctionsAppendixE.UsefulIntegralsE.1AlgebraicFunctionsE.2TrigonometricFunctionsE.3GammaFunctionsE.4EllipticIntegralsAppendixF.DifferentialRelationsinCurvilinearCoordinateSystemsF.1CylindricalCoordinatesF.2SphericalCoordinatesAppendixG.AProofoftheRelationΣµχ2µ=Σµχ'2µSelectedReferencesBibliographyProductdetailsNo.ofpages:592Language:EnglishCopyright:©AcademicPress1965Published:January1,1965Imprint:AcademicPresseBookISBN:9781483272818AbouttheAuthorJerryB.MarionRatingsandReviewsWriteareviewTherearecurrentlynoreviewsfor"ClassicalDynamicsofParticlesandSystems" 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