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Analytical Mechanics

by: Fowles, Grant R.; Cassiday, George L.

Analytical Mechanics

by: Fowles, Grant R.; Cassiday, George L.

ISBN 13:
9780534494926
ISBN 10:
0534494927
Edition: 7th
Format: Hardcover
Copyright: 03/19/2004
Publisher: Cengage Learning

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Summary

Master introductory mechanics with ANALYTICAL MECHANICS! Direct and practical, this physics text is designed to help you grasp the challenging concepts of physics. Specific cases are included to help you master theoretical material. Numerous worked examples found throughout increase your problem-solving skills and prepare you to succeed on tests.

1 Fundamental Concepts: Vectors

(46)

1.1 Introduction

(1)

1.2 Measure of Space and Time: Units and Dimensions

(7)

1.3 Vectors

(6)

1.4 The Scalar Product

(4)

1.5 The Vector Product

(3)

1.6 An Example of the Cross Product: Moment of a Force

(1)

1.7 Triple Products

(2)

1.8 Change of Coordinate System: The Transformation Matrix

(5)

1.9 Derivative of a Vector

(1)

1.10 Position Vector of a Particle: Velocity and Acceleration in Rectangular Coordinates

(5)

1.11 Velocity and Acceleration in Plane Polar Coordinates

(3)

1.12 Velocity and Acceleration in Cylindrical and Spherical Coordinates

(8)

2 Newtonian Mechanics: Rectilinear Motion of a Particle

(35)

2.1 Newton's Law of Motion: Historical Introduction

(13)

2.2 Rectilinear Motion: Uniform Acceleration Under a Constant Force

(3)

2.3 Forces that Depend on Position: The Concepts of Kinetic and Potential Energy

(6)

2.4 Velocity-Dependent Forces: Fluid Resistance and Terminal Velocity

(6)

2.5 Vertical Fall Through a Fluid: Numerical Solution

(7)

3 Oscillations

(62)

3.1 Introduction

(2)

3.2 Linear Restoring Force: Harmonic Motion

(9)

3.3 Energy Considerations in Harmonic Motion

(3)

3.4 Damped Harmonic Motion

(10)

3.5 Phase Space

106

(7)

3.6 Forced Harmonic Motion: Resonance

113

(12)

3.7 The Nonlinear Oscillator: Method of Successive Approximations

125

(4)

3.8 The Nonlinear Oscillator: Chaotic Motion

129

(6)

3.9 Nonsinusoidal Driving Force: Fourier Series

135

(9)

4 General Motion of a Particle in Three Dimensions

144

(40)

4.1 Introduction: General Principles

144

(7)

4.2 The Potential Energy Function in Three-Dimensional Motion: The Del Operator

151

(5)

4.3 Forces of the Separable Type: Projectile Motion

156

(11)

4.4 The Harmonic Oscillator in Two and Three Dimensions

167

(6)

4.5 Motion of Charged Particles in Electric and Magnetic Fields

173

(3)

4.6 Constrained Motion of a Particle

176

(8)

5 Noninertial Reference Systems

184

(34)

5.1 Accelerated Coordinate Systems and Inertial Forces

184

(5)

5.2 Rotating Coordinate Systems

189

(7)

5.3 Dynamics of a Particle in a Rotating Coordinate System

196

(5)

5.4 Effects of Earth's Rotation

201

(6)

5.5 Motion of a Projectile in a Rotating Cylinder

207

(5)

5.6 The Foucault Pendulum

212

(6)

6 Gravitation and Central Forces

218

(57)

6.1 Introduction

218

(5)

6.2 Gravitational Force between a Unifirm Sphere and a Particle

223

(2)

6.3 Kepler's Laws of Planetary Motion

225

(1)

6.4 Kepler's Second Law: Equal Areas

226

(3)

6.5 Kepler's First Law: The Law of Ellipses

229

(9)

6.6 Kepler's Third Law: The Harmonic Law

238

(6)

6.7 Potential Energy in a Gravitational Field: Gravitational Potential

244

(6)

6.8 Potential Energy in a General Central Field

250

(1)

6.9 Energy Equation of an Orbit in a Central Field

251

(1)

6.10 Orbital Energies in an Inverse-Square Field

251

(6)

6.11 Limits of the Radial Motion: Effective Potential

257

(3)

6.12 Nearly Circular Orbits in Central Fields: Stability

260

(2)

6.13 Apsides and Apsidal Angles for Nearly Circular Orbits

262

(2)

6.14 Motion in an Inverse-Square Repulsive Field: Scattering of Alpha Particles

264

(11)

7 Dynamics of Systems of Particles

275

(48)

7.1 Introduction: Center of Mass and Linear Momentum of a System

275

(3)

7.2 Angular Momentum and Kinetic Energy of a System

278

(5)

7.3 Motion of Two Interacting Bodies: The Reduced Mass

283

(5)

7.4 The Restricted Three-Body Problem

288

(15)

7.5 Collisions

303

(3)

7.6 Oblique Collisions and Scattering: Comparison of Laboratory and Center of Mass Coordinates

306

(6)

7.7 Motion of a Body with Variable Mass: Rocket Motion

312

(11)

8 Mechanics of Rigid Bodies: Planar Motion

323

(38)

8.1 Center of Mass of a Rigid Body

323

(5)

8.2 Rotation of a Rigid Body about a Fixed Axis: Moment of Inertia

328

(2)

8.3 Calculation of the Moment of Inertia

330

(8)

8.4 The Physical Pendulum

338

(6)

8.5 The Angular Momentum of a Rigid Body in Laminar Motion

344

(3)

8.6 Examples of the Laminar Motion of a Rigid Body

347

(7)

8.7 Impulse and Collisions Involving Rigid Bodies

354

(7)

9 Motion of Rigid Bodies in Three Dimensions

361

(56)

9.1 Rotation of a Rigid Body about an Arbitrary Axis: Moments and Products of Inertia Angular Momentum and Kinetic Energy

361

(10)

9.2 Principal Axes of a Rigid Body

371

(10)

9.3 Euler's Equations of Motion of a Rigid Body

381

(2)

9.4 Free Rotation of a Rigid Body: Geometric Description of the Motion

383

(1)

9.5 Free Rotation of a Rigid Body with an Axis of Symmetry: Analytical Treatment

384

(7)

9.6 Description of the Rotation of a Rigid Body Relative to a Fixed Coordinate System: The Eulerian Angles

391

(6)

9.7 Motion of a Top

397

(4)

9.8 The Energy Equation and Nutation

401

(6)

9.9 The Gyrocompass

407

(2)

9.10 Why Lance Doesn't Fall Over (Mostly)

409

(8)

10 Lagrangian Mechanics

417

(48)

10.1 Hamilton's Variational Principle: An Example

419

(4)

10.2 Generalized Coordinates

423

(3)

10.3 Calculating Kinetic and Potential Energies in Terms of Generalized Coordinates: An Example

426

(4)

10.4 Lagrange's Equations of Motion for Conservative Systems

430

(1)

10.5 Sone Applications of Lagrange's Equations

431

(7)

10.6 Generalized Momenta: Ignorable Coordinates

438

(6)

10.7 Forces of Constraint: Lagrange Multipliers

444

(5)

10.8 D'Alembert's Principle: Generalized Forces

449

(6)

10.9 The Hamiltonian Function: Hamilton's Equations

455

(10)

11 Dynamics of Oscillating Systems

465

11.1 Potential Energy and Equilibrium: Stability

465

(4)

11.2 Oscillation of a System with One Degree of Freedom about a Position of Stable Equilibrium

469

(3)

11.3 Coupled Harmonic Oscillators: Normal Coordinates

472

(21)

11.4 General Theory of Vibrating Systems

493

(5)

11.5 Vibration of a Loaded String or Linear Array of Coupled Harmonic Oscillators

498

(7)

11.6 Vibration of a Continuous System: The Wave Equation

505

Appendix A Units

A-1

Appendix B Complex Numbers and Identities

A-4

Appendix C Conic Sections

A-7

Appendix D Service Expansions

A-11

Appendix E Special Functions

A-13

Appendix F Curvilinear Coordinates

A-15

Appendix G Fourier Series

A-17

Appendix H Matrices

A-19

Appendix I Software Tools: Mathcad and Mathematica

A-24

Answers to Selected Odd-Numbered Problems

ANS-1

Selected References

R-1

Index

I-1

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Analytical Mechanics

Analytical Mechanics

9780534494926

0534494927

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Analytical Mechanics

Analytical Mechanics

9780534494926

0534494927

Summary

Table of Contents

Supplemental Materials

Write a Review

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