Amazon no longer offers textbook rentals. We do!

Classical Dynamics of Particles and Systems

by: Thornton, Stephen T.; Marion, Jerry B.

Classical Dynamics of Particles and Systems

by: Thornton, Stephen T.; Marion, Jerry B.

ISBN 13:
9780030973024
ISBN 10:
0030973023
Edition: 4th
Format: Hardcover
Copyright: 01/17/1995
Publisher: Brooks Cole
Newer Edition

Rent

Sorry, this item is currently unavailable.

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Extend or Purchase Your Rental at Any Time

Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.

Summary

This best-selling classical mechanics text, written for the advanced undergraduate one- or two-semester course, provides a complete account of the classical mechanics of particles, systems of particles, and rigid bodies. The authors make extensive use of vector calculus to explore topics; coverage also includes the Lagrangian formulation of mechanics. Modern notation and terminology are used throughout in support of the text's objective: to facilitate the transition to the quantum theory of physics.

1 MATRICES, VECTORS, AND VECTOR CALCULUS

(47)

1.1 Introduction

(1)

1.2 Concept of a Scalar

(1)

1.3 Coordinate Transformations

(3)

1.4 Properties of Rotation Matrices

(3)

1.5 Matrix Operations

(3)

1.6 Further Definitions

(2)

1.7 Geometrical Significance of Transformation Matrices

(6)

1.8 Definitions of a Scalar and a Vector in Terms of Transformation Properties

(1)

1.9 Elementary Scalar and Vector Operations

(1)

1.10 Scalar Product of Two Vectors

(3)

1.11 Unit Vectors

(1)

1.12 Vector Product of Two Vectors

(5)

1.13 Differentiation of a Vector with Respect to a Scalar

(1)

1.14 Examples of Derivatives-Velocity and Acceleration

(4)

1.15 Angular Velocity

(3)

1.16 Gradient Operator

(3)

1.17 Integration of Vectors

(3)

Problems

(4)

2 NEWTONIAN MECHANICS-SINGLE PARTICLE

(59)

2.1 Introduction

(1)

2.2 Newton's Laws

(4)

2.3 Frames of Reference

(1)

2.4 The Equation of Motion for a Particle

(22)

2.5 Conservation Theorems

(6)

2.6 Energy

(6)

2.7 Rocket Motion

(9)

2.8 Limitations of Newtonian Mechanics

(2)

Problems

(8)

3 OSCILLATIONS

107

(46)

3.1 Introduction

107

(1)

3.2 Simple Harmonic Oscillator

108

(3)

3.3 Harmonic Oscillations in Two Dimensions

111

(3)

3.4 Phase Diagrams

114

(2)

3.5 Damped Oscillations

116

(9)

3.6 Sinusoidal Driving Forces

125

(6)

3.7 Physical Systems

131

(1)

3.8 Electrical Oscillations

132

(5)

3.9 Principle of Superposition-Fourier Series

137

(3)

3.10 The Response of Linear Oscillators to Impulsive Forcing Functions (optional)

140

(8)

Problems

148

(5)

4 NONLINEAR OSCILLATIONS AND CHAOS

153

(36)

4.1 Introduction

153

(2)

4.2 Nonlinear Oscillations

155

(4)

4.3 Phase Diagrams for Nonlinear Systems

159

(3)

4.4 Plane Pendulum

162

(5)

4.5 Jumps, Hysteresis, and Phase Lags

167

(4)

4.6 Chaos in a Pendulum

171

(6)

4.7 Mapping

177

(4)

4.8 Chaos Identification

181

(5)

Problems

186

(3)

5 GRAVITATION

189

(24)

5.1 Introduction

189

(2)

5.2 Gravitational Potential

191

(9)

5.3 Lines of Force and Equipotential Surfaces

200

(1)

5.4 When Is the Potential Concept Useful?

201

(3)

5.5 Ocean Tides

204

(6)

Problems

210

(3)

6 SOME METHODS IN THE CALCULUS OF VARIATIONS

213

(19)

6.1 Introduction

213

(1)

6.2 Statement of the Problem

214

(2)

6.3 Euler's Equation

216

(6)

6.4 The "Second Form" of the Euler Equation

222

(3)

6.5 Functions with Several Dependent Variables

225

(1)

6.6 Euler Equations When Auxiliary Conditions Are Imposed

225

(3)

6.7 The (XXX) Notation

228

(2)

Problems

230

(2)

7 HAMILTON'S PRINCIPLE-LAGRANGIAN AND HAMILTONIAN DYNAMICS

232

(59)

7.1 Introduction

232

(1)

7.2 Hamilton's Principle

233

(4)

7.3 Generalized Coordinates

237

(4)

7.4 Lagrange's Equations of Motion in Generalized Coordinates

241

(11)

7.5 Lagrange's Equations with Undetermined Multipliers

252

(6)

7.6 Equivalence of Lagrange's and Newton's Equations

258

(3)

7.7 Essence of Lagrangian Dynamics

261

(2)

7.8 A Theorem Concerning the Kinetic Energy

263

(1)

7.9 Conservation Theorems Revisited

264

(5)

7.10 Canonical Equations of Motion-Hamiltonian Dynamics

269

(8)

7.11 Some Comments Regarding Dynamical Variables and Variational Calculations in Physics

277

(2)

7.12 Phase Space and Liouville's Theorem (optional)

279

(3)

7.13 Virial Theorem (optional)

282

(3)

Problems

285

(6)

8 CENTRAL-FORCE MOTION

291

(42)

8.1 Introduction

291

(1)

8.2 Reduced Mass

291

(2)

8.3 Conservation Theorems-First Integrals of the Motion

293

(2)

8.4 Equations of Motion

295

(4)

8.5 Orbits in a Central Field

299

(1)

8.6 Centrifugal Energy and the Effective Potential

300

(3)

8.7 Planetary Motion-Kepler's Problem

303

(6)

8.8 Orbital Dynamics

309

(8)

8.9 Apsidal Angles and Precession (optional)

317

(4)

8.10 Stability of Circular Orbits (optional)

321

(7)

Problems

328

(5)

9 DYNAMICS OF A SYSTEM OF PARTICLES

333

(48)

9.1 Introduction

333

(1)

9.2 Center of Mass

334

(2)

9.3 Linear Momentum of the System

336

(4)

9.4 Angular Momentum of the System

340

(4)

9.5 Energy of the System

344

(6)

9.6 Elastic Collisions of Two Particles

350

(7)

9.7 Kinematics of Elastic Collisions

357

(6)

9.8 Inelastic Collisions

363

(4)

9.9 Cross Sections

367

(5)

9.10 Rutherford Scattering Formula

372

(2)

Problems

374

(7)

10 MOTION IN A NONINERTIAL REFERENCE FRAME

381

(23)

10.1 Introduction

381

(1)

10.2 Rotating Coordinate Systems

382

(3)

10.3 Centrifugal and Coriolis Forces

385

(4)

10.4 Motion Relative to the Earth

389

(13)

Problems

402

(2)

11 DYNAMICS OF RIGID BODIES

404

(55)

11.1 Introduction

404

(1)

11.2 Inertia Tensor

405

(5)

11.3 Angular Momentum

410

(4)

11.4 Principal Axes of Inertia

414

(5)

11.5 Moments of Inertia for Different Body Coordinate Systems

419

(4)

11.6 Further Properties of the Inertia Tensor

423

(8)

11.7 Eulerian Angles

431

(4)

11.8 Euler's Equations for a Rigid Body

435

(5)

11.9 Force-Free Motion of a Symmetric Top

440

(5)

11.10 Motion of a Symmetric Top with One Point Fixed

445

(6)

11.11 Stability of Rigid-Body Rotations

451

(3)

Problems

454

(5)

12 COUPLED OSCILLATIONS

459

(44)

12.1 Introduction

459

(1)

12.2 Two Coupled Harmonic Oscillators

460

(4)

12.3 Weak Coupling

464

(2)

12.4 General Problem of Coupled Oscillations

466

(6)

12.5 Orthogonality of the Eigenvectors (optional)

472

(2)

12.6 Normal Coordinates

474

(8)

12.7 Molecular Vibrations

482

(4)

12.8 Three Linearly Coupled Plane Pendula-An Example of Degeneracy

486

(3)

12.9 The Loaded String

489

(10)

Problems

499

(4)

13 CONTINUOUS SYSTEMS; WAVES

503

(33)

13.1 Introduction

503

(1)

13.2 Continuous String as a Limiting Case of the Loaded String

504

(3)

13.3 Energy of a Vibrating String

507

(3)

13.4 Wave Equation

510

(2)

13.5 Forced and Damped Motion

512

(3)

13.6 General Solutions of the Wave Equation

515

(3)

13.7 Separation of the Wave Equation

518

(6)

13.8 Phase Velocity, Dispersion, and Attenuation

524

(5)

13.9 Group Velocity and Wave Packets

529

(4)

Problems

533

(3)

14 THE SPECIAL THEORY OF RELATIVITY

536

(43)

14.1 Introduction

536

(1)

14.2 Galilean Invariance

537

(2)

14.3 Lorentz Transformation

539

(6)

14.4 Experimental Verification of the Special Theory

545

(3)

14.5 Relativistic Doppler Effect

548

(3)

14.6 Twin Paradox

551

(2)

14.7 Relativistic Momentum

553

(3)

14.8 Energy

556

(4)

14.9 Spacetime and Four-Vectors

560

(8)

14.10 Lagrangian Function in Special Relativity

568

(2)

14.11 Relativistic Kinematics

570

(4)

Problems

574

(5)

APPENDICES

A TAYLOR'S THEOREM

579

(6)

Problems

583

(2)

B ELLIPTIC INTEGRALS

585

(5)

Problems

589

(1)

C ORDINARY DIFFERENTIAL EQUATIONS OF SECOND ORDER

590

(9)

C.1 Linear Homogeneous Equations

590

(4)

C.2 Linear Inhomogeneous Equations

594

(3)

Problems

597

(2)

D USEFUL FORMULAS

599

(5)

D.1 Binomial Expansion

599

(1)

D.2 Trigonometric Relations

600

(1)

D.3 Trigonometric Series

601

(1)

D.4 Exponential and Logarithmic Series

601

(1)

D.5 Complex Quantities

601

(1)

D.6 Hyperbolic Functions

602

(1)

Problems

603

(1)

E Useful Integrals

604

(4)

E.1 Algebraic Functions

604

(1)

E.2 Trigonometric Functions

605

(1)

E.3 Gamma Functions

606

(2)

F Differential Relations in Different Coordinate Systems

608

(4)

F.1 Rectangular Coordinates

608

(1)

F.2 Cylindrical Coordinates

608

(2)

F.3 Spherical Coordinates

610

(2)

G A "Proof" of the Relation XXX = XXX

612

(2)

H Numerical Solution for Example 2.7

614

(3)

Selected References

617

(2)

Bibliography

619

(4)

Answers to Even-Numbered Problems

623

(7)

Index

630

Amazon no longer offers textbook rentals. We do!

Classical Dynamics of Particles and Systems

Classical Dynamics of Particles and Systems

9780030973024

0030973023

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Classical Dynamics of Particles and Systems

Classical Dynamics of Particles and Systems

9780030973024

0030973023

Summary

Table of Contents

Supplemental Materials

Write a Review

Related Products