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Classical Dynamics of Particles & Systems

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  • Àú : Marion
  • ÃâÆÇ»ç : Thomson Learning
  • ¹ßÇà : 2003³â 07¿ù 07ÀÏ
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  • ISBN : 9780534408961
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Matrices, Vectors, and Vector Calculusp. 1
Introductionp. 1
Concept of a Scalarp. 2
Coordinate Transformationsp. 3
Properties of Rotation Matricesp. 6
Matrix Operationsp. 9
Further Definitionsp. 12
Geometrical Significance of Transformation Matricesp. 14
Definitions of a Scalar and a Vector in Terms of Transformation Propertiesp. 20
Elementary Scalar and Vector Operationsp. 20
Scalar Product of Two Vectorsp. 21
Unit Vectorsp. 23
Vector Product of Two Vectorsp. 25
Differentiation of a Vector with Respect to a Scalarp. 29
Examples of Derivatives--Velocity and Accelerationp. 30
Angular Velocityp. 34
Gradient Operatorp. 37
Integration of Vectorsp. 40
Problemsp. 43
Newtonian Mechanics--Single Particlep. 48
Introductionp. 48
Newton's Lawsp. 49
Frames of Referencep. 53
The Equation of Motion for a Particlep. 55
Conservation Theoremsp. 76
Energyp. 82
Limitations of Newtonian Mechanicsp. 88
Problemsp. 90
Oscillationsp. 99
Introductionp. 99
Simple Harmonic Oscillatorp. 100
Harmonic Oscillations in Two Dimensionsp. 104
Phase Diagramsp. 106
Damped Oscillationsp. 108
Sinusoidal Driving Forcesp. 117
Physical Systemsp. 123
Principle of Superposition--Fourier Seriesp. 126
The Response of Linear Oscillators to Impulsive Forcing Functions (Optional)p. 129
Problemsp. 138
Nonlinear Oscillations and Chaosp. 144
Introductionp. 144
Nonlinear Oscillationsp. 146
Phase Diagrams for Nonlinear Systemsp. 150
Plane Pendulump. 155
Jumps, Hysteresis, and Phase Lagsp. 160
Chaos in a Pendulump. 163
Mappingp. 169
Chaos Identificationp. 174
Problemsp. 178
Gravitationp. 182
Introductionp. 182
Gravitational Potentialp. 184
Lines of Force and Equipotential Surfacesp. 194
When Is the Potential Concept Useful?p. 195
Ocean Tidesp. 198
Problemsp. 204
Some Methods in the Calculus of Variationsp. 207
Introductionp. 207
Statement of the Problemp. 207
Euler's Equationp. 210
The "Second Form" of the Euler Equationp. 216
Functions with Several Dependent Variablesp. 218
Euler Equations When Auxiliary Conditions Are Imposedp. 219
The [delta] Notationp. 224
Problemsp. 226
Hamilton's Principle--Lagrangian and Hamiltonian Dynamicsp. 228
Introductionp. 228
Hamilton's Principlep. 229
Generalized Coordinatesp. 233
Lagrange's Equations of Motion in Generalized Coordinatesp. 237
Lagrange's Equations with Undetermined Multipliersp. 248
Equivalence of Lagrange's and Newton's Equationsp. 254
Essence of Lagrangian Dynamicsp. 257
A Theorem Concerning the Kinetic Energyp. 258
Conservation Theorems Revisitedp. 260
Canonical Equations of Motion--Hamiltonian Dynamicsp. 265
Some Comments Regarding Dynamical Variables and Variational Calculations in Physicsp. 272
Phase Space and Liouville's Theorem (Optional)p. 274
Virial Theorem (Optional)p. 277
Problemsp. 280
Central-Force Motionp. 287
Introductionp. 287
Reduced Massp. 287
Conservation Theorems--First Integrals of the Motionp. 289
Equations of Motionp. 291
Orbits in a Central Fieldp. 295
Centrifugal Energy and the Effective Potentialp. 296
Planetary Motion--Kepler's Problemp. 300
Orbital Dynamicsp. 305
Apsidal Angles and Precession (Optional)p. 312
Stability of Circular Orbits (Optional)p. 316
Problemsp. 323
Dynamics of a System of Particlesp. 328
Introductionp. 328
Center of Massp. 329
Linear Momentum of the Systemp. 331
Angular Momentum of the Systemp. 336
Energy of the Systemp. 339
Elastic Collisions of Two Particlesp. 345
Kinematics of Elastic Collisionsp. 352
Inelastic Collisionsp. 358
Scattering Cross Sectionsp. 363
Rutherford Scattering Formulap. 369
Rocket Motionp. 371
Problemsp. 378
Motion in a Nonintertial Reference Framep. 387
Introductionp. 387
Rotating Coordinate Systemsp. 388
Centrifugal and Coriolis Forcesp. 391
Motion Relative to the Earthp. 395
Problemsp. 408
Dynamics of Rigid Bodiesp. 411
Introductionp. 411
Simple Planar Motionp. 412
Inertia Tensorp. 415
Angular Momentump. 419
Principal Axes of Inertiap. 424
Moments of Inertia for Different Body Coordinate Systemsp. 428
Further Properties of the Inertia Tensorp. 433
Eulerian Anglesp. 440
Euler's Equations for a Rigid Bodyp. 444
Force-Free Motion of a Symmetric Topp. 448
Motion of a Symmetric Top with One Point Fixedp. 454
Stability of Rigid-Body Rotationsp. 460
Problemsp. 463
Coupled Oscillationsp. 468
Introductionp. 468
Two Coupled Harmonic Oscillatorsp. 469
Weak Couplingp. 473
General Problem of Coupled Oscillationsp. 475
Orthogonality of the Eigenvectors (Optional)p. 481
Normal Coordinatesp. 483
Molecular Vibrationsp. 490
Three Linearly Coupled Plane Pendula--an Example of Degeneracyp. 495
The Loaded Stringp. 498
Problemsp. 507
Continuous Systems; Wavesp. 512
Introductionp. 512
Continuous String as a Limiting Case of the Loaded Stringp. 513
Energy of a Vibrating Stringp. 516
Wave Equationp. 520
Forced and Damped Motionp. 522
General Solutions of the Wave Equationp. 524
Separation of the Wave Equationp. 527
Phase Velocity, Dispersion, and Attenuationp. 533
Group Velocity and Wave Packetsp. 538
Problemsp. 542
Special Theory of Relativityp. 546
Introductionp. 546
Galilean Invariancep. 547
Lorentz Transformationp. 548
Experimental Verification of the Special Theoryp. 555
Relativistic Doppler Effectp. 558
Twin Paradoxp. 561
Relativistic Momentump. 562
Energyp. 566
Spacetime and Four-Vectorsp. 569
Lagrangian Function in Special Relativityp. 578
Relativistic Kinematicsp. 579
Problemsp. 583
Appendices
Taylor's Theoremp. 589
Problemsp. 593
Elliptic Integralsp. 594
Elliptic Integrals of the First Kindp. 594
Elliptic Integrals of the Second Kindp. 595
Elliptic Integrals of the Third Kindp. 595
Problemsp. 598
Ordinary Differential Equations of Second Orderp. 599
Linear Homogeneous Equationsp. 599
Linear Inhomogeneous Equationsp. 603
Problemsp. 606
Useful Formulasp. 608
Binomial Expansionp. 608
Trigonometric Relationsp. 609
Trigonometric Seriesp. 610
Exponential and Logarithmic Seriesp. 610
Complex Quantitiesp. 611
Hyperbolic Functionsp. 611
Problemsp. 612
Useful Integralsp. 613
Algebraic Functionsp. 613
Trigonometric Functionsp. 614
Gamma Functionsp. 615
Differential Relations in Different Coordinate Systemsp. 617
Rectangular Coordinatesp. 617
Cylindrical Coordinatesp. 617
Spherical Coordinatesp. 619
A "Proof" of the Relation [characters not reproducible] = [characters not reproducible]p. 621
Numerical Solution for Example 2.7p. 623
Selected Referencesp. 626
Bibliographyp. 628
Answers to Even-Numbered Problemsp. 633
Indexp. 643
Table of Contents provided by Ingram. All Rights Reserved.

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1. Matrices, Vectors, and Vector Calculus. 2. Newtonian Mechanics--Single Particle. 3. Oscillations. 4. Nonlinear Oscillations and Chaos. 5. Gravitation. 6. Some Methods in the Calculus of Variations. 7. Hamilton's Principle--Lagrangian and Hamiltonian Dynamics. 8. Central-Force Motion. 9. Dynamics of a System of Particles. 10. Motion in a Noninertial Reference Frame. 11. Dynamics of Rigid Bodies. 12. Coupled Oscillations. 13. Continuous Systems: Waves. 14. The Special Theory of Relativity. Appendices. Selected References. Bibliography. Answers to Even-Numbered Problems.

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