Prefacexiii
Chapter1INTRODUCTIONTOTHEMECHANICALUNIVERSE(Program1)
1.1TheCopernicanRevolution
1.2UnitsandDimensions5
1.3AFinalWord10
Chapter2THELAWOFFALLINGBODIES(Program2)13
2.1Aristotle'sDescriptionofMotion13
2.2DoHeavyBodiesFallFasterThanLighterOnes?15
2.3MedievalLawsofFallingBOdies15
2.4"The"LawofFallingBodies20
2.5TheAve'rageSpeedofaFallingBody25
2.6InstantaneousSpeed26
2.7Acceleration32
2.8AFinalWord36
Chapter3DERIVATIVES(Program3)39
3.1TheDevelopmentofDifferentialCalculus39
3.2TheTangentLine-DerivativeConnection41
3.3RulesofDifferentiation47
3.4DerivativesofSpecialFunctions58
3.5AFinalWord67
Chapter4INERTIA(Program4)69
4.1IftheEarthMoves:AristotelianObjections6g
4.2TheEarthMoves:Galileo'sLawofInertia72
4.3RelativeMotion75
4.4ProjectileMotion:AConsequenceofInertia77
4.5AFinalWord80
Chapter5VECTORS(Program5)81
5.1TheRiseofVectorAnalysis81
5.2Vectors-AGeometricView82
5.3Vectors:AnAnalyticView96
5.4TheCrossProduct106
5.5AFinalWord110
Chapter6NEWTON'SLAWS(Program6)111
6.1TheEndoftheConfusion111
6.2Newton'sLawsofMotion112
6.3UnitsofMass,Momentum,andForce117
6.4ProjectileMotion:AnApplicationof-Newton'sSecondLaw119
6.5AFinalWord127
Chapter7INTEGRATION(Program7)129
7.1Antidifferentiation,theReverseofDifferentiation129
7.2AntidifferentiationandQuadrature133
7.3TheLeibnizIntegralNotation137
7.4ApplicationsoftheSecondFundamentalTheoremtoPhysics145
7.5AFinalWord150
Appendix1TheFundamentalTheoremsofCalculus151
Appendix2QuadratureofaHyperbolicSegment.TheLogarithmFunction152
Chapter8THEAPPLEANDTHEMOON(Program8)159
8.1TheGenesisofanIdea159
8.2TheLawofUniversalGravitation160
8.3AccelerationofGravityontheEarth?65
8.4WhytheMoonDoesn'tFalltotheEarth168
8.5AFinalWord172
Chapter9MOVINGINCIRCLES(Program9)175
9.1ThePerfectionofCircularMotion175
9.2DerivativesofVectorFunctions177
9.3UniformCircularMotion183
9.4CircularOrbits187
9.5MotionalongSpaceCurves189
9.6AFinalWord191
Chapter10FORCES(Program10)193
10.1TheFundamentalForces193
10.2GravitationalandElectricForces195
10.3ContactForces198
10.4ApplicationofNewton'sLaws202
10.5Friction210
10.6AFinalWord215
Chapter11GRAVITY,ELECTRICITY,ANDMAGNETISM(Program11)217
11.1FindingtheConnectionbetweenElectricityandMagnetism217
11.2Faraday'sFields219
11.3APredictionfromElectromagnetism224
11.4AFinalWord226
Chapter12THEMILLIKANOIL-DROPEXPERIMENT(Program12)229
12.1TheDiscoveryoftheElectron229
12.2MotioninaResistiveMedium233
12.3TheOii-DropExperiment239
12.4AFinalWord243
Chapter13THELAWOFCONSERVATIONOFENERGY(Program13)245
13.1TowardanIdeaofEnergy245
13.2WorkandPotentialEnergy247
13.3TheLawofConservationofEnergy252
13.4HeatandEnergy260
13.5AFinalWord263
Chapter14ENERGYANDSTABILITY(Program14)267
14.1FormsofEnergy267
14.2GravitationalPotentialEnergy274
14.3PotentialEnergyandStability278
14.4AFinalWord284
Chapter15TEMPERATUREANDTHEGASLAWS(Program45)287
15.1TemperatureandPressure287
15.2TheGasLawsofBoyle,Charles,andGay-Lussac293
15.3TheIdeal-GasLaw295
15.4TemperatureandEnergy297
15.5AFinalWord299
Chapter16THEENGINEOFNATURE(Program46)301
16.1TheAgeofSteam301
16.2WorkandthePressure-VolumeDiagram303
16.3TheFirstLawofThermodynamics309
16.4AdiabaticandIsothermalProcesses312
16.5TheSecondLawofThermodynamics316
16.6TheCarnotEngine319
16.7AFinalWord324
Chapter17ENTROPY(Program47)327
17.1TowardanUnderstandingofEntropy327
17.2EnginesandEntropy330
17.3EntropyandtheSecondLawofThermodynamics336
17.4AnImplicationoftheEntropyPrinciple338
17.5AFinalWord341
Chapter18THEQUESTFORLOWTEMPERATURES(Program48)343
18.1CoolingOff343
18.2TheStatesofMatter344
18.3BehaviorofWater349
18.4LiquefactionofGases351
18.5TheJoule-ThomsonEffect355
18.6AFinalWord357
Chapter19THECONSERVATIONOFMOMENTUM{Program15)359
19.1TheUniverseasaMachine359
19.2Newton'sLawsinRetrospect360
19.3TheLawofConservationofMomentum364
19.4ApplicationsofConservationofMomentum368
19.5CollisionForcesandTimes376
19.6AFinalWord378
Chapter20HARMONICMOTION(Program16)379
20.1FindingaClockThatWouldn'tGetSeasick379
20.2SimpleHarmonicMotion381
20.3EnergyConservationandSimpleHarmonicMotion387
20.4InitialConditions390
20.5TheSimplePendulum393
20.6AFinalWord396
Chapter21RESONANCE(Program17)399
21.1ForcedOscillations399
21.2DescribingResonance401
21.3SwingingandSingingWiresintheWind408
21.4AFinalWord409
Chapter22COUPLEDOSCILLATORSANDWAVES(Program18)413
22.1NewtonandtheSpeedofSound413
22.2CoupledOscillators415
22.3WaterWavesandWaveCharacteristics417
22.4WaveSpeed420
22.5Sound426
22.6SoundIntensities428
22.7SoundandHeat429
22.8AFinalWord430
Chapter23ANGULARMOMENTUM(Program19)433
23.1TheSearchforOrder433
23.2TheLawofEqualAreas437
23.3AngularMomentum440
23.4TorqueandAngularMomentum444
23.5VorticesandFirestorms447
23.6AngularMomentumandtheArchitectureoftheHeavens450
23.7AFinalWord454
Chapter24GYROSCOPES(Program20)457
24.1AnAncientQuestion457
24.2TheGyroscope459
24.3TheGyrocompass466
24.4AngularVelocityofPrecession469
24.5TheEarthasaGyrosc.ope473
24.6AFinalWord474
Chapter25KEPLER'SLAWSANDTHECONICSECTIONS(Program21)477
25.1TheQuestforPrecision477
25.2Kepler'sLaws479
25.3ConicSections482
25.4TheEllipse485
25.5TheConicsandEccentricity489
25.6CartesianEquationsforConicSections492
25.7AFinalWord494
Chapter26SOLVINGTHEKEPLERPROBLEM(Program22)497
26.1Settingthe*Stage497
26.2PolarCoordinatesandtheUnitVectorsrando499
26.3SolutionoftheKeplerProblem502
26.4AFinalWord504
Chapter27ENERGYANDECCENTRICITY(Program23)507
27.lCelestialOmens:Comets507
27.2EnergyinSpace508
27.3EnergyandEccentricity511
27.4OrbitsandEccentricity513
27.5PlAnetaryMotionandEffectivePotential516
27.6CalculatingtheOrbitfromInitialConditions519
27.7AFinalWord522
Chapter28NAVIGATINGINSPACE(Program24)525
28.1FreewaysintheSky525
28.2NavigatinginSpace526
28.3TransferOrbits529
28.4GravityAssist534
28.5AFinalWord537
Chapter29LOOSEENDSANDBLACKHOLES(Program25)539
29.1Kepler'sThirdLaw539
29.2TheEarth-SunandEarth-MoonSystems541
29.3TheTides543
29.4ThePrincipleofEquivalence546
29.5Einstein'sTheoryofGravity548
29.6BlackHoles549
29.7AFinalWord550
Chapter30THEHARMONYOFTHESPHERES:ANOVERVIEWOFTHE
MECHANICALUNIVERSE(Program26)553
30.1WindingUpTheMechanicalUniverse553
30.2ThePhysicsoftheHeavensandEarth554
30.3TheLanguageofPhysics556
30.4TheConservationLawsoftheMechanicalUniverse559
30.5AFinalWord561
AppendixATHEINTERNATIONALSYSTEMOFUNITS563
AppendixBCONVERSIONFACTORS565
AppendixCFORMULASFROMALGEBRA,GEOMETRY,ANDTRIGONOMETRY569
AppendixDASTRONOMICALDATA571
AppendixEPHYSICALCONSTANTS573
SELECTEDBIBLIOGRAPHY575
Index579
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