the foundations of celestial mechanics - g. w. collins

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1、TheFoundationsOfCelestialMechanicsByGeorgeW.Collins,IICaseWesternReserveUniversity©2004bythePachartFoundationdbaPachartPublishingHouseandreprintedbypermission.iiToC.M.Huffer,whotaughtittheoldway,butwhocaredthatwelearn.iiiivTableofContentsListofFigures…………………………………………………

2、…...………….viiiPreface…………………………………………………………………………..ixPrefacetotheWEBedition…………………………………………………….xiiChapter1:IntroductionandMathematicsReview……………………………..11.1TheNatureofCelestialMechanics………………………………..11.2Scalars,Vectors,Tensors,MatricesandTheirProducts………….2a.Scalars.………

3、………………………………………………2b.Vectors……………………………………...…………………3c.TensorsandMatrices………………………………………….41.3Commutatively,Associativity,andDistributivity….……………….81.4Operators……………………………………...…………………....8a.CommonDelOperators……………………………………...13ChapterlExercises……………………………………………………..14

4、Chapter2:CoordinateSystemsandCoordinateTransformations………………152.1OrthogonalCoordinateSystems…………………………………….162.2AstronomicalCoordinateSystems…………………………………..17a.TheRightAscension–DeclinationCoordinateSystem………17b.EclipticCoordinates…………………………………………..19c.Alt-AzimuthCoordi

5、nateSystem……………………………...192.3GeographicCoordinateSystems…………………………………….20a.TheAstronomicalCoordinateSystem………………………..20b.TheGeodeticCoordinateSystem……………………………..20c.TheGeocentricCoordinateSystem…………………………...212.4CoordinateTransformations…………………………………………212.5TheEulerianA

6、ngles…………………………………………………272.6TheAstronomicalTriangle…………………………………………..282.7Time………………………………………………………………….34Chapter2Exercises………………………………………………………38Chapter3:TheBasicsofClassicalMechanics…………………………………..393.1Newton'sLawsandtheConservationofMomentumandEnergy…..393.2VirtualW

7、ork,D'Alembert'sPrinciple,andLagrange'sEquationsofMotion.……………………………………………………………...423.3TheHamiltonian…………………………...………………………...47Chapter3:Exercises…………………………………………………….50vChapter4:PotentialTheory……………………………………………………...514.1TheScalarPotentialFieldandtheGravitationalField

8、………………524.2Poisson'sandLaplace'sEquations…………………………………...534.3MultipoleExpansionofthePotential………………………………..56