经典力学与天体力学中的数学问题 【正版图书】 下载 pdf 百度网盘 epub 免费 2025 电子书 mobi 在线

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BasicPrinciplesofClassicalMechanics

.NewtonianMechanics

..Space，Time，Motion

..2Newton-LaplacePrincipleofDeterminacy

..3PrincipleofRelativity

..4PrincipleofRelativityandForcesofInertia

..5BasicDynamicalQuantities.ConservationLaws

.2LagrangianMechanics

.2.PreliminaryRemarks

.2.2VariationsandExtremals

.2.3LagrangesEquations

.2.4PoincaresEquations

.2.5MotionwithConstraints

.3HamiltonianMechanics

.3.SymplecticStructuresandHamiltonsEquations

.3.2GeneratingFunctions

.3.3SymplecticStructureoftheCotangentBundle

.3.4TheProblemofnPointVortices

.3.5ActioninthePhaseSpace

.3.6IntegralInvariant

.3.7ApplicationstoDynamicsofIdealFluid

.4VakonomicMechanics

.4.LagrangesProblem

.4.2VakonomicMechanics

.4.3PrincipleofDeterminacy

.4.4HamiltonsEquationsinRedundantCoordinates

.5HamiltonianFormalismwithConstraints

.5.DiracsProblem

.5.2Duality

.6RealizationofConstraints

.6.VariousM

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Thisworkdescribesthefundamentalprinciples-problems-andmethodsofclassicalmechanics.Themainattentionisdevotedtothemathematicalsideofthesubject.Theauthorsheendeoredtogiveanexpositionstressingtheworkingapparatusofclassicalmechanics.Thebookissignificantlyexpandedcomparedtothepreviousedition.Theauthorsheaddedtwochaptersonthevariationalprinciplesandmethodsofclassicalmechanicsaswellasontensorinvariantsofequationsofdynamics.Moreover-variousothersectionshebeenrevised-addedorexpanded.Themainpurposeofthebookistoacquaintthereaderwithclassicalmechanicsasawhole-inbothitsclassicalanditscontemporaryaspects.Thebookaddressesallmathematicians-physicistsandengineers.