Engineering Mechanics Statics and Dynamics

Author C.L. Best, E.W. Nelson, W.G. McLean
Publisher McGraw Hill
ISBN 9780070461932
Schaums Outlines of Theory and Problems of Engineering Mechanics Statics and Dynamics

PROBLEMS AND SECTIONS ALSO FOUND IN THE ix
COMPANION SCHAUM'S ELECTRONIC TUTOR
Chapter 1 VECTORS 1 (18)
1.1 Definitions
1.2 Addition of Two Vectors
1.3 Subtraction of a Vector
1.4 Zero Vector
1.5 Composition of Vectors
1.6 Multiplication of Vectors by Scalars
1.7 Orthogonal Triad of Unit Vectors
1.8 Position Vector
1.9 Dot or Scalar Product
1.10 The Cross or Vector Product
1.11 Vector Calculus
1.12 Dimensions and Units
Chapter 2 OPERATIONS WITH FORCES 19 (12)
2.1 The Moment of a Force
2.2 A Couple
2.3 The Moment of a Couple
2.4 Replacing a Single Force
2.5 Coplanar Force Systems
2.6 Notes
Chapter 3 RESULTANTS OR COPLANAR FORCE 31 (15)
SYSTEMS
3.1 Coplanar Forces
3.2 Concurrent System
3.3 Parallel System
3.4 Nonconcurrent, Nonparallel System
3.5 Resultant of Distributed Force Systems
Chapter 4 RESULTANTS OF NONCOPLANAR FORCE 46 (10)
SYSTEMS
4.1 Noncoplanar Force Systems
4.2 Resultants of a Noncoplanar Force
System
4.3 Concurrent System
4.4 Parallel System
4.5 Nonconcurrent, Nonparallel System
Chapter 5 EQUILIBRIUM OF COPLANAR FORCE 56 (24)
SYSTEMS
5.1 Equilibrium of a Coplanar Force System
5.2 Two-Force Members
5.3 Concurrent System
5.4 Parallel System
5.5 Nonconcurrent, Nonparallel System
5.6 Remarks--Free Body Diagrams
Chapter 6 EQUILIBRIUM OF NONCOPLANAR FORCE 80 (17)
SYSTEMS
6.1 Equilibrium of a Noncoplanar Force
System
6.2 Parallel System
6.3 Concurrent System
6.4 Nonconcurrent, Nonparallel System
Chapter 7 TRUSSES AND CABLES 97 (18)
7.1 Trusses and Cables
7.2 Trusses
7.3 Cables
Chapter 8 FORCES IN BEAMS 115(12)
8.1 Beams
8.2 Types of Beams
8.3 Shear and Moment
8.4 Shear and Moment Diagrams
8.5 Slope of the Shear Diagram
8.6 Change in Shear
8.7 Slope of the Moment Diagram
8.8 Change in Moment
Chapter 9 FRICTION 127(28)
9.1 General Concepts
9.2 Laws of Friction
9.3 Jackscrew
9.4 Belt Friction and Brake Bands
9.5 Rolling Resistance
Chapter 10 FIRST MOMENTS AND CENTROIDS 155(29)
10.1 Centroid of an Assemblage
10.2 Centroid of a Continuous Quantity
10.3 Theorems of Pappus and Guldinus
10.4 Center of Pressure
Chapter 11 VIRTUAL WORK 184(11)
11.1 Virtual Displacement and Virtual Work
11.2 Equilibrium
11.3 Stable Equilibrium
11.4 Unstable Equilibrium
11.5 Neutral Equilibrium
11.6 Summary of Equilibrium
Chapter 12 KINEMATICS OF A PARTICLE 195(34)
12.1 Kinematics
12.2 Rectilinear Motion
12.3 Curvilinear Motion
12.4 Rectangular Components
12.5 Tangential and Normal Components
12.6 Radial and Transverse Components
12.7 Units
Chapter 13 DYNAMICS OF A PARTICLE 229(32)
13.1 Newton's Laws of Motion
13.2 Units
13.3 Acceleration
13.4 D'Alembert's Principle
13.5 Problems in Dynamics
Chapter 14 KINEMATICS OF A RIGID BODY IN 261(37)
PLANE MOTION
14.1 Plane Motion of a Rigid Body
14.2 Translation
14.3 Rotation
14.4 Instantaneous Axis of Rotation
14.5 Coriolis' Acceleration
Chapter 15 MOMENTS OF INERTIA 298(32)
15.1 Axial Moment of Inertia of an Element
of Area
15.2 Polar Moment of Inertia of an Element
of Area
15.3 Product of Inertia of an Element of
Area
15.4 Axial Moment of Inertia of an Area
15.5 Radius of Gyration of an Area
15.6 Polar Moment of Inertia of an Area
15.7 Product of Inertia of an Area
15.8 Parallel Axis Theorem
15.9 Composite Area
15.10 Rotated Set of Axes
15.11 Mohr's Circle
15.12 Axial Moment of Inertia of an
Element of Mass
15.13 Axial Moment of Inertia of a Mass
15.14 Radius of Gryation of a Mass
15.15 Product of Inertia of a Mass
15.16 Parallel Axis Theorem for a Mass
15.17 Composite Mass
Chapter 16 DYNAMICS OF A RIGID BODY IN PLANE 330(64)
MOTION
16.1 Vector Equations of Plane Motion
16.2 Scalar Equations of Plane Motion
16.3 Pictorial Representation of the
Equations
16.4 Translation of a Rigid Body
16.5 Rotation of a Rigid Body
16.6 Center of Percussion
16.7 The Inertia-Force Method for Rigid
Bodies
Chapter 17 WORK AND ENERGY 394(30)
17.1 Work
17.2 Special Cases
17.3 Power
17.4 Efficiency
17.5 Kinetic Energy of a Particle
17.6 Work-Energy Relations for a Particle
17.7 Kinetic Energy T of a Rigid Body in
Translation
17.8 Kinetic Energy T of a Rigid Body in
Rotation
17.9 Kinetic Energy T of a Body in Plane
Motion
17.10 Potential Energy
17.11 Work-Energy Relations for a Rigid
Body
17.12 Law of Conservation of Energy
Chapter 18 IMPULSE AND MOMENTUM 424(38)
18.1 Linear Impulse-Momentum Relation for
a Particle
18.2 Linear Impulse-Momentum Relation for
an Assemblage of Particles
18.3 Moment of Momentum H(0)
18.4 Moment of Relative Momentum H(0)
18.5 Corresponding Scalar Equations
18.6 Units
18.7 Conservation of Linear Momentum
18.8 Conservation of Angular Momentum
18.9 Impact
18.10 Variable Mass
Chapter 19 MECHANICAL VIBRATIONS 462(31)
19.1 Definitions
19.2 Degrees of Freedom
19.3 Simple Harmonic Motion
19.4 Multicomponent Systems
19.5 Units
Appendix A SI UNITS 493(2)
Appendix B FIRST MOMENTS AND CENTROIDS 495(2)
Appendix C COMPUTER SOLUTIONS TO SELECTED 497(4)
PROBLEMS
Appendix D SAMPLE SCREENS FROM THE COMPANION 501(16)
SCHAUM'S ELECTRONIC TUTOR
INDEX 517

Physics for Game Developers
Beginning Math and Physics for Game Programmers
Other Physics Books
Download

Applied Mathematical Methods In Theoretical Physics

Contents
Preface IX
Introduction 1
1 Function Spaces, Linear Operators and Green’s Functions 5
1.1 Function Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Orthonormal System of Functions . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Linear Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Eigenvalues and Eigenfunctions . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 The Fredholm Alternative . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Self-adjoint Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Green’s Functions for Differential Equations . . . . . . . . . . . . . . . . . 16
1.8 Review of Complex Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.9 Review of Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 Integral Equations and Green’s Functions 33
2.1 Introduction to Integral Equations . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Relationship of Integral Equations with Differential Equations and Green’s
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Sturm–Liouville System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 Green’s Function for Time-Dependent Scattering Problem . . . . . . . . . . 48
2.5 Lippmann–Schwinger Equation . . . . . . . . . . . . . . . . . . . . . . . . 52
2.6 Problems for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3 Integral Equations of Volterra Type 63
3.1 Iterative Solution to Volterra Integral Equation of the Second Kind . . . . . 63
3.2 Solvable cases of Volterra Integral Equation . . . . . . . . . . . . . . . . . 66
3.3 Problems for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4 Integral Equations of the Fredholm Type 75
4.1 Iterative Solution to the Fredholm Integral Equation of the Second Kind . . 75
4.2 Resolvent Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3 Pincherle–Goursat Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Fredholm Theory for a Bounded Kernel . . . . . . . . . . . . . . . . . . . . 86
4.5 Solvable Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.6 Fredholm Integral Equation with a Translation Kernel . . . . . . . . . . . . 95
4.7 System of Fredholm Integral Equations of the Second Kind . . . . . . . . . 100
4.8 Problems for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Hilbert–Schmidt Theory of Symmetric Kernel 109
5.1 Real and Symmetric Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2 Real and Symmetric Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.3 Bounds on the Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.4 Rayleigh Quotient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.5 Completeness of Sturm–Liouville Eigenfunctions . . . . . . . . . . . . . . 129
5.6 Generalization of Hilbert–Schmidt Theory . . . . . . . . . . . . . . . . . . 131
5.7 Generalization of Sturm–Liouville System . . . . . . . . . . . . . . . . . . 138
5.8 Problems for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6 Singular Integral Equations of Cauchy Type 149
6.1 Hilbert Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.2 Cauchy Integral Equation of the First Kind . . . . . . . . . . . . . . . . . . 153
6.3 Cauchy Integral Equation of the Second Kind . . . . . . . . . . . . . . . . 157
6.4 Carleman Integral Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.5 Dispersion Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.6 Problems for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7 Wiener–Hopf Method and Wiener–Hopf Integral Equation 177
7.1 The Wiener–Hopf Method for Partial Differential Equations . . . . . . . . . 177
7.2 Homogeneous Wiener–Hopf Integral Equation of the Second Kind . . . . . 191
7.3 General Decomposition Problem . . . . . . . . . . . . . . . . . . . . . . . 207
7.4 Inhomogeneous Wiener–Hopf Integral Equation of the Second Kind . . . . 216
7.5 Toeplitz Matrix and Wiener–Hopf Sum Equation . . . . . . . . . . . . . . . 227
7.6 Wiener–Hopf Integral Equation of the First Kind and Dual Integral Equations 235
7.7 Problems for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
8 Nonlinear Integral Equations 249
8.1 Nonlinear Integral Equation of Volterra type . . . . . . . . . . . . . . . . . 249
8.2 Nonlinear Integral Equation of Fredholm Type . . . . . . . . . . . . . . . . 253
8.3 Nonlinear Integral Equation of Hammerstein type . . . . . . . . . . . . . . 257
8.4 Problems for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
9 Calculus of Variations: Fundamentals 263
9.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
9.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
9.3 Euler Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
9.4 Generalization of the Basic Problems . . . . . . . . . . . . . . . . . . . . . 272
9.5 More Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
9.6 Differential Equations, Integral Equations, and Extremization of Integrals . . 278
9.7 The Second Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
9.8 Weierstrass–Erdmann Corner Relation . . . . . . . . . . . . . . . . . . . . 297
9.9 Problems for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
10 Calculus of Variations: Applications 303
10.1 Feynman’s Action Principle in Quantum Mechanics . . . . . . . . . . . . . 303
10.2 Feynman’s Variational Principle in Quantum Statistical Mechanics . . . . . 308
10.3 Schwinger–Dyson Equation in Quantum Field Theory . . . . . . . . . . . . 312
10.4 Schwinger–Dyson Equation in Quantum Statistical Mechanics . . . . . . . 329
10.5 Weyl’s Gauge Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
10.6 Problems for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
Bibliography 365
Index 373

Another Mathematics Books
Another Physics Books
Download

Manga Guide to Physics

Megumi is an all-star athlete, but she's a failure when it comes to physics class. And she can't concentrate on her tennis matches when she's worried about the questions she missed on the big test! Luckily for her, she befriends Ryota, a patient physics geek who uses real-world examples to help her understand classical mechanics-and improve her tennis game in the process!

You'll also learn how to:

Apply Newton's three laws of motion to real-life problems

Determine how objects will move after a collision

Draw vector diagrams and simplify complex problems using trigonometry

Calculate how an object's kinetic energy changes as its potential energy increases

If you're mystified by the basics of physics or you just need a refresher, The Manga Guide to Physics will get you up to speed in a lively, quirky, and practical way.

In The Manga Guide to Physics, you'll follow alongside Megumi as she learns about the physics of everyday objects like roller skates, slingshots, braking cars, and tennis serves. In no time, you'll master tough concepts like momentum and impulse, parabolic motion, and the relationship between force, mass, and acceleration.


Table of Contents
Preface
Prologue: Does Physics Bother You?

1: Law of Action and Reaction
2: Force and Motion
3: Momentum
4: Energy

Epilogue
Appendix: Making Sense of Units
Index

Another Manga Books
Another Comic Books
Another Physics Books
Download