经典力学新基础

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.