Analytical Mechanics

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

• ISBN13: 9780534494926
• ISBN10: 0534494927
• Edition: 7th
• Format: Hardcover
• Copyright: 2004-03-19
• Publisher: Cengage Learning

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.

Table of Contents

1 Fundamental Concepts: Vectors	1	(46)
1.1 Introduction	1	(1)
1.2 Measure of Space and Time: Units and Dimensions	2	(7)
1.3 Vectors	9	(6)
1.4 The Scalar Product	15	(4)
1.5 The Vector Product	19	(3)
1.6 An Example of the Cross Product: Moment of a Force	22	(1)
1.7 Triple Products	23	(2)
1.8 Change of Coordinate System: The Transformation Matrix	25	(5)
1.9 Derivative of a Vector	30	(1)
1.10 Position Vector of a Particle: Velocity and Acceleration in Rectangular Coordinates	31	(5)
1.11 Velocity and Acceleration in Plane Polar Coordinates	36	(3)
1.12 Velocity and Acceleration in Cylindrical and Spherical Coordinates	39	(8)
2 Newtonian Mechanics: Rectilinear Motion of a Particle	47	(35)
2.1 Newton's Law of Motion: Historical Introduction	47	(13)
2.2 Rectilinear Motion: Uniform Acceleration Under a Constant Force	60	(3)
2.3 Forces that Depend on Position: The Concepts of Kinetic and Potential Energy	63	(6)
2.4 Velocity-Dependent Forces: Fluid Resistance and Terminal Velocity	69	(6)
2.5 Vertical Fall Through a Fluid: Numerical Solution	75	(7)
3 Oscillations	82	(62)
3.1 Introduction	82	(2)
3.2 Linear Restoring Force: Harmonic Motion	84	(9)
3.3 Energy Considerations in Harmonic Motion	93	(3)
3.4 Damped Harmonic Motion	96	(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