经典力学新基础

图书标准信息

• 作者 [美]赫斯腾萨（D.hestense） 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030236272
• 定价 99.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 703页
• 字数 886千字
• 正文语种 英语
• 丛书 国外物理名著系列

【内容简介】

　　Thisbookprovidesanintroductiontogeometricalgebraasanunifiedlanguageforphysicsandmathematics.Itcontainesextensiveapplicationstoclassicalmechanicsinatextbookformatsuitableforcoursesatanintermediatelevel.Thetextissupportedbymorethan200diagramstohelpdevelopgeometricalandphysicalintuition.Besidescoveringthestandardmaterialforacourseonthemechanicsofparticlesandrigidbodies,thebookintroducesnew,coordinatefreemethodsforrotationaldynamicsandorbitalmechanics,developingthesesubjectstoalevelwellbeyondthatofothertextbooks.Thesemethodshavebeenwidelyappliedinrecentyearstobiomechanicsandrobotics,tocomputervisionandgeometricdesign,toorbitalmechanicsingovernmentalandindustrialspaceprograms,aswellastootherbranchesofphysics.Thebookappliesthemtothemajorperturbationsinthesolarsystem,includingtheplanetaryperturbationsofMercurysperihelion.
　　Geometricalgebraintegratesconventionalvectoralgebra(alongwithitsestablishednotations)intoasystemwithalltheadvantagesofquaternionsandspinors.Thus,itincreasesthepowerofthemathematicallanguageofclassicalmechanicswhilebringingitclosertothelanguageofquantummechanics.Thisbooksystematicallydevelopspurelymathematicalapplicationsofgeometricalgebrausefulinphysics,includingextensiveapplicationstolinearalgebraandtransformationgroups.Itcontainssufficientmaterialforacourseonmathematicaltopicsalone.
　　Thesecondeditionhasbeenexpandedbynearlyahundredpagesonrelativisticmechanics.Thetreatmentisuniqueinitsexclusiveuseofgeometricalgebraandinitsdetailedtreatmentofspacetimemaps.collisions,motioninuniformfieldsandrelativisticprecession.ItconformswithEinsteinsviewthattheSpecialTheoryofRelativityistheculminationofdevelopmentsinclassicalmechanics.

【目录】

Preface
Chapter1：OriginsofGeometricAlgebra
1-1.GeometryasPhysics
1-2.NumberandMagnitude
1-3.DirectedNumbers
1-4.TheInnerProduct
1-5.TheOuterProduct
1-6.SynthesisandSimplification
1-7.AxiomsforGeometricAlgebra

Chapter2：DevelopmentsinGeometricAlgebra
2-1.BasicIdentitiesandDefinitions
2-2.TheAlgebraofaEuclideanPlane
2-3.TheAlgebraofEuclidean3-Space
2-4.Directions，ProjectionsandAngles
2-5.TheExponentialFunction
2-6.AnalyticGeometry
2-7.FunctionsofaScalarVariable
2-8.DirectionalDerivativesandLineIntegrals

Chapter3：MechanicsofaSingleParticle
3-1.NewtonsProgram
3-2.ConstantForce
3-3.ConstantForcewithLinearDrag
3-4.ConstantForcewithQuadraticDrag
3-5.FluidResistance
3-6.ConstantMagneticField
3-7.UniformElectricandMagneticFields
3-8.LinearBindingForce
3-9.ForcedOscillations
3-10.ConservativeForcesandConstraints

Chapter4：CentralForcesandTwo-ParticleSystems
4-1.AngularMomentum
4-2.DynamicsfromKinematics
4-3.TheKeplerProblem
4-4.TheOrbitinTime
4-5.ConservativeCentralForces
4-6.Two-particleSystems
4-7.ElasticCollisions
4-8.ScatteringCrossSections

Chapter5：OperatorsandTransformations
5-1.LinearOperatorsandMatrices
5-2.SymmetricandSkewsymmetricOperators
5-3.TheArithmeticofReflectionsandRotations
5-4.TransformationGroups
5-5.RigidMotionsandFramesofReference
5-6.MotioninRotatingSystems

Chapter6：Many-ParticleSystems
6-1.GeneralPropertiesofMany-ParticleSystems
6-2.TheMethodofLagrange
6-3.CoupledOscillationsandWaves
6-4.TheoryofSmallOscillations
6-5.TheNewtonianManyBodyProblem

Chapter7：RigidBodyMechanics
7-1.RigidBodyModeling
7-2.RigidBodyStructure
7-3.TheSymmetricalTop
7-4.IntegrableCasesofRotationalMotion
7-5.RollingMotion
7-6.ImpulsiveMotion

Chapter8：CelestialMechanics
8-1.GravitationalForces，FieldsandTorques
8-2.PerturbationsofKeplerMotion
8-3.PerturbationsintheSolarSystem
8-4.SpinorMechanicsandPerturbationTheory

Chapter9：RelativisticMechanics
9-1.SpacetimeandItsRepresentations
9-2.SpacetimeMapsandMeasurements
9-3.RelativisticParticleDynamics
9-4.Energy-MomentumConservation
9-5.RelativisticRigidBodyMechanics

Appendix
ASphericalTrigonometry
BEllipticFunctions
CUnits，ConstantsandData
HintsandSolutionsforSelectedExercises
References
Index