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Classical dynamics of particles and systems

Author: Stephen T Thornton; Jerry B Marion
Publisher: Boston, MA : Brooks/Cole, Cengage Learning, ©2008.
Edition/Format:   Print book : English : 5th edition ; international student editionView all editions and formats
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Document Type: Book
All Authors / Contributors: Stephen T Thornton; Jerry B Marion
ISBN: 9780534408961 0534408966 9780495556107 0495556106
OCLC Number: 908630642
Notes: Marion's name appears first on earlier edition.
Description: xvi, 656 pages : illustrations ; 24 cm
Contents: 1 Matrices, Vectors, and Vector Calculus 1 --
1.2 Concept of a Scalar 2 --
1.3 Coordinate Transformations 3 --
1.4 Properties of Rotation Matrices 6 --
1.5 Matrix Operations 9 --
1.7 Geometrical Significance of Transformation Matrices 14 --
1.8 Definitions of a Scalar and a Vector in Terms of Transformation Properties 20 --
1.9 Elementary Scalar and Vector Operations 20 --
1.10 Scalar Product of Two Vectors 21 --
1.11 Unit Vectors 23 --
1.12 Vector Product of Two Vectors 25 --
1.13 Differentiation of a Vector with Respect to a Scalar 29 --
1.14 Examples of Derivatives --
Velocity and Acceleration 30 --
1.15 Angular Velocity 34 --
1.16 Gradient Operator 37 --
1.17 Integration of Vectors 40 --
2 Newtonian Mechanics --
Single Particle 48 --
2.2 Newton's Laws 49 --
2.3 Frames of Reference 53 --
2.4 The Equation of Motion for a Particle 55 --
2.5 Conservation Theorems 76 --
2.6 Energy 82 --
2.7 Limitations of Newtonian Mechanics 88 --
3 Oscillations 99 --
3.2 Simple Harmonic Oscillator 100 --
3.3 Harmonic Oscillations in Two Dimensions 104 --
3.4 Phase Diagrams 106 --
3.5 Damped Oscillations 108 --
3.6 Sinusoidal Driving Forces 117 --
3.7 Physical Systems 123 --
3.8 Principle of Superposition --
Fourier Series 126 --
3.9 The Response of Linear Oscillators to Impulsive Forcing Functions (Optional) 129 --
4 Nonlinear Oscillations and Chaos 144 --
4.2 Nonlinear Oscillations 146 --
4.3 Phase Diagrams for Nonlinear Systems 150 --
4.4 Plane Pendulum 155 --
4.5 Jumps, Hysteresis, and Phase Lags 160 --
4.6 Chaos in a Pendulum 163 --
4.7 Mapping 169 --
4.8 Chaos Identification 174 --
5 Gravitation 182 --
5.2 Gravitational Potential 184 --
5.3 Lines of Force and Equipotential Surfaces 194 --
5.4 When Is the Potential Concept Useful? 195 --
5.5 Ocean Tides 198 --
6 Some Methods in the Calculus of Variations 207 --
6.2 Statement of the Problem 207 --
6.3 Euler's Equation 210 --
6.4 The "Second Form" of the Euler Equation 216 --
6.5 Functions with Several Dependent Variables 218 --
6.6 Euler Equations When Auxiliary Conditions Are Imposed 219 --
6.7 The [delta] Notation 224 --
7 Hamilton's Principle --
Lagrangian and Hamiltonian Dynamics 228 --
7.2 Hamilton's Principle 229 --
7.3 Generalized Coordinates 233 --
7.4 Lagrange's Equations of Motion in Generalized Coordinates 237 --
7.5 Lagrange's Equations with Undetermined Multipliers 248 --
7.6 Equivalence of Lagrange's and Newton's Equations 254 --
7.7 Essence of Lagrangian Dynamics 257 --
7.8 A Theorem Concerning the Kinetic Energy 258 --
7.9 Conservation Theorems Revisited 260 --
7.10 Canonical Equations of Motion --
Hamiltonian Dynamics 265 --
7.11 Some Comments Regarding Dynamical Variables and Variational Calculations in Physics 272 --
7.12 Phase Space and Liouville's Theorem (Optional) 274 --
7.13 Virial Theorem (Optional) 277 --
8 Central-Force Motion 287 --
8.2 Reduced Mass 287 --
8.3 Conservation Theorems --
First Integrals of the Motion 289 --
8.4 Equations of Motion 291 --
8.5 Orbits in a Central Field 295 --
8.6 Centrifugal Energy and the Effective Potential 296 --
8.7 Planetary Motion --
Kepler's Problem 300 --
8.8 Orbital Dynamics 305 --
8.9 Apsidal Angles and Precession (Optional) 312 --
8.10 Stability of Circular Orbits (Optional) 316 --
9 Dynamics of a System of Particles 328 --
9.2 Center of Mass 329 --
9.3 Linear Momentum of the System 331 --
9.4 Angular Momentum of the System 336 --
9.5 Energy of the System 339 --
9.6 Elastic Collisions of Two Particles 345 --
9.7 Kinematics of Elastic Collisions 352 --
9.8 Inelastic Collisions 358 --
9.9 Scattering Cross Sections 363 --
9.10 Rutherford Scattering Formula 369 --
9.11 Rocket Motion 371 --
10 Motion in a Nonintertial Reference Frame 387 --
10.2 Rotating Coordinate Systems 388 --
10.3 Centrifugal and Coriolis Forces 391 --
10.4 Motion Relative to the Earth 395 --
11 Dynamics of Rigid Bodies 411 --
11.2 Simple Planar Motion 412 --
11.3 Inertia Tensor 415 --
11.4 Angular Momentum 419 --
11.5 Principal Axes of Inertia 424 --
11.6 Moments of Inertia for Different Body Coordinate Systems 428 --
11.7 Further Properties of the Inertia Tensor 433 --
11.8 Eulerian Angles 440 --
11.9 Euler's Equations for a Rigid Body 444 --
11.10 Force-Free Motion of a Symmetric Top 448 --
11.11 Motion of a Symmetric Top with One Point Fixed 454 --
11.12 Stability of Rigid-Body Rotations 460 --
12 Coupled Oscillations 468 --
12.2 Two Coupled Harmonic Oscillators 469 --
12.3 Weak Coupling 473 --
12.4 General Problem of Coupled Oscillations 475 --
12.5 Orthogonality of the Eigenvectors (Optional) 481 --
12.6 Normal Coordinates 483 --
12.7 Molecular Vibrations 490 --
12.8 Three Linearly Coupled Plane Pendula --
an Example of Degeneracy 495 --
12.9 The Loaded String 498 --
13 Continuous Systems; Waves 512 --
13.2 Continuous String as a Limiting Case of the Loaded String 513 --
13.3 Energy of a Vibrating String 516 --
13.4 Wave Equation 520 --
13.5 Forced and Damped Motion 522 --
13.6 General Solutions of the Wave Equation 524 --
13.7 Separation of the Wave Equation 527 --
13.8 Phase Velocity, Dispersion, and Attenuation 533 --
13.9 Group Velocity and Wave Packets 538 --
14 Special Theory of Relativity 546 --
14.2 Galilean Invariance 547 --
14.3 Lorentz Transformation 548 --
14.4 Experimental Verification of the Special Theory 555 --
14.5 Relativistic Doppler Effect 558 --
14.6 Twin Paradox 561 --
14.7 Relativistic Momentum 562 --
14.8 Energy 566 --
14.9 Spacetime and Four-Vectors 569 --
14.10 Lagrangian Function in Special Relativity 578 --
14.11 Relativistic Kinematics 579 --
A Taylor's Theorem 589 --
B.1 Elliptic Integrals of the First Kind 594 --
B.2 Elliptic Integrals of the Second Kind 595 --
B.3 Elliptic Integrals of the Third Kind 595 --
C Ordinary Differential Equations of Second Order 599 --
C.1 Linear Homogeneous Equations 599 --
C.2 Linear Inhomogeneous Equations 603 --
D.1 Binomial Expansion 608 --
D.2 Trigonometric Relations 609 --
D.3 Trigonometric Series 610 --
D.4 Exponential and Logarithmic Series 610 --
D.5 Complex Quantities 611 --
D.6 Hyperbolic Functions 611 --
E.1 Algebraic Functions 613 --
E.2 Trigonometric Functions 614 --
E.3 Gamma Functions 615 --
F Differential Relations in Different Coordinate Systems 617 --
F.1 Rectangular Coordinates 617 --
F.2 Cylindrical Coordinates 617 --
F.3 Spherical Coordinates 619.
Responsibility: Stephen T. Thornton ; Jerry B. Marion.

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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 Read more...

 
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