CHAPTER 1 KINEMATICS OF A PARTICLE

1.1 Introduction

1.2 Rectilinear Motion of a Particle: Single Degree of Freedom

1.3 Classification of Kinematics Problems

1.4 The Inverse Dynamics Problem

Sample Problems 1.1-1.2

Problems 1.1-1.24

1.5 The Direct Dynamics Problem: Rectilinear Motion When the Acceleration is Given

1.5.1 Classification of Differential Equations

1.5.2 Separable First-Order Scalar Differential Equations

Sample Problem 1.7

Problems 1.25-1.55

1.5.4 Solution of a Linear First-Order differential Equation by Use of an Integrating Factor

Sample Problem 1.8

1.5.5 Second-Order Linear First-Order Equations

Sample Problem 1.9

1.5.6 Numerical Solution of Differential Equations

Sample Problem 1.10

Problems 1.56-1.65

1.6 Curvilinear Motion of a Particle

1.6.1 Vector Differential Equation

1.6.2 Projectile Motion

Sample Problems 1.11-1.14

Problems 1.66-1.87

1.7 Normal and Tangential Coordinates

1.7.1 Circular Motion

Sample Problems 1.15-1.17

1.7.2 Normal and Tangential Coordinates in Three Dimensions

Sample Problem 1.18

Problems 1.88-1.102

1.8 Radial and Transverse Coordinates (Polar Coordinates)

Sample Problems 1.19-1.22

Problems 1.103-1.118

1.9 Three-Dimensional Coordinate Systems: Cylindrical and Spherical Coordinates

1.9.1 Cylindrical Coordinates

Sample Problem 1.23

1.9.2 Spherical Coordinates

Sample Problem 1.24

Problems 1.119-1.128

1.10 Relative Rectilinear Motion of Several Particles

Sample Problems 1.25-1.26

Problems 1.129-1.41

1.11 General Relative Motion Between Particles

Sample Problems 1.27-1.29

1.11.1 Navigation Using Relative Velocity

Sample Problem 1.30

Problems 1.142-1.159

1.12 Dependent Motions Between Two or More Particles

Sample Problems 1.31-1.33

Problems 1.160-1.170

1.13 Parametric Equations in Kinematics

1.13.1 Trajectories Expressed as Function of Parameters

Sample Problems 1.34-1.35

1.13.2 Parametric Equations for Three-Dimensional Trajectories

Sample Problem 1.36

Problem 1.171-1.178 

CHAPTER 2 KINETICS OF PARTICLES

2.1 Introduction

2.1.1 Equations of Motion for a Particle

2.2 Solution Strategy for Particle Dynamics

2.2.1 Review of the Concepts of static and Kinetic Friction

Sample Problems 2.1-2.2

2.2.2 Alternative Selection of Coordinate System

Sample Problems 2.3-2.6

2.2.3 Determination of the Direction of the Normal and Friction Forces

Sample Problems 2.7-2.8

Problems 2.1-2.34

2.3 Discontinuity and Sigularity Functions

Sample Problems 2.9-2.10

2.4 Special Problem

Problems 2.35-2.44

2.5 Normal and Tangential Coordinates

Sample Problems 2.11-2.13

Problems 2.45-2.66

2.6 Two-Dimensional Parametric Equation of Dynamics

Sample Problems 2.14-2.15

Problems 2.67-2.72

2.7 Polar Coordinates

Sample Problems 2.16-2.17

Problems 2.73-2.86

2.7.1 Angular Momentum of a Particle

2.7.2 Central-Force Motion

Sample Problems 2.18-2.19

Problems 2.87-2.96

2.8 Three-Dimensional Particle Dynamics in Curvilinear Coordinates

2.8.1 Cylindrical Coordinates

Sample Problems 2.20-2.21

2.8.2 Spherical Coordinates

Sample Problem 2.22

2.8.3 Parametric Equations in Tangential, Normal, and Binormal Coordinates

Sample Problem 2.97-2.116

2.9 Detection of modeling and Constraint Errors in Complex Particle Dynamics Problems

Sample Problem 2.24 

CHAPTER 3 WORK-ENERGY AND IMPULSE-MOMENTUM FIRST INTEGRALS OF MOTION

3.1 Introduction

3.2 Power, Work, and Energy

3.2.1 Work of a Spring Force

3.2.2 Work of the Gravitational Attraction Froce Between Two Masses

Sample Problems 3.1-3.5

Sample Problem 3.6

Problems 3.1-3.45

3.3 conservative Forces and Potential Energy

3.4 Conservation of Energy

Sample Problems 3.7-3.8

Problems 3.46-3.70

3.5 Principle of Impulse and Momentum

3.5.1 Impulse and Momentum of Several Particles

Sample Problems 3.9-3.10

Problems 3.71-3.93

3.6 Impact

3.6.1 Direct Central Impact

Sample Problem 3.11

3.6.2 Oblique Central Impact

3.6.3 Impact with a Stationary Object

Sample Problems 3.12-3.13

Problems 3.94-3.116 

CHAPTER 4 SYSTEM OF PARTICLES

4.1 Introduction

4.2 General Equations for a System of Particles

4.3 Center of Mass of a System of Particles

Sample Problems 4.1-4.3

Problems 4.1-4.21

4.4 Kinetic Energy of a System of Particles

4.5 Work-Energy and Conservation of Energy of a System of Particles

4.6 Impulse and Momentum of a System of Particles

Sample Problem 4.4

Problems 4.22-4.42

4.7 Mass Flows

4.7.1 Steady Mass Flow

Sample Problem 4.6

Problems 4.43-4.57 

CHAPTER 5 KINEMATICS OF RIGID BODIES

5.1 Introduction

5.2 Translation of a Rigid Body

5.3 Rotation About a Fixed Axis

Sample Problem 5.1

5.4 Planar Pure Rotation About an Axis Perpendicular to the Plan of Motion

5.4.1 Vector Relations for Rotation in a Plane

5.4.2 Direct Vector Solution for Angular Velocity and Angular Acceleration

5.4.3 Constraints to the Motion

Sample Problems 5.2-5.8

Problems 5.1-5.21

5.5 General Plane Motion

5.5.1 Absolute and Relative Velocities in Plane Motion of a Rigid Body

5.5.2 Experimental Motion Data

Sample Problems 5.9-5.12

5.5.3 Direct Vector Method to Obtain the Angular Velocity

Problems 5.22-5.42

5.6 Instantaneous Center of Rotation in Plane Motion

Sample Problems 5.13-5.15

5.7 Instantaneous Center of Rotation Between Two Rigid Bodies

Problems 5.43-5.59

5.8 Absolute and Relative Acceleration of a Rigid Body in Plane Motion

5.8.1 Alternate Solution of the Acceleration of Rigid Bodies

Sample Problems 5.16-5.19

Problems 5.60-5.73

5.9 Kinematics of a System of Rigid Bodies

Sample Problem 5.20

Problems 5.74-5.82

5.10 Analysis of Plane Motion in Terms of a Parameter

Sample Problems 5.21-5.23

Problems 5.83-5.93

5.11 General Three-Dimensional Motion of a Rigid Body

5.11.1 Linear and Angular Acceleration

5.11.2 Constraints to the General Three-Dimensional Motion of a Rigid Body

5.11.3 Rigid Body with a Fixed Point in Space

5.11.4 Other Constraints

Sample Problems 5.24-5.26

Problems 5.94-5.108

5.12 Instantaneous Helical Axis, or Screw Axis

5.12.1 Motion of a Rigid Body Having a Fixed Point in Space

Sample Problem 5.27

5.13 Instantaneous Helical Axis of Rotation Between Two Rigid Bodies

Sample Problem 5.28

Problems 5.1009-5.113

5.14 Motion with Respect to a Rotating Reference Frame or Coordinate System

5.14.1 Sliding Contact

Sample Problems 5.29-5.31

Problems 5.114-5.124 

CHAPTER 6 DYNAMICS OF RIGID BODIES IN PLANE MOTION

6.1 Introduction

6.2 Linear and Angular Momentum

6.2.1 Angular Momentum About a Fixed Point on a Rigid Body

6.3 Equations of Motion for Rigid Bodies in Plane Motion

Sample Problems 6.1-6.4

6.4 Constraints on the Motion

Sample Problem 6.5

6.4.1 Rolling Without Sliding

6.4.2 Rolling and Sliding

Sample Problems 6.6-6.8

6.5 Computational Methods for Plane Dynamic Systems

Sample Problem 6.9

Problems 6.1-6.27

6.6 Systems of Rigid Bodies or Particles

Sample Problems 6.10-6.12

Problems 6.28-6.75

6.7 D'Alembert's Principle

Problems 6.76-6.97 

CHAPTER 7 POWER, WORK, ENERGY, IMPULSE, AND MOMENTUM OF A RIGID BODY

7.1 Power, Work, and Energy, of a Rigid Body

7.1.1 Work Done by a Couple

Sample Problem

7.2 Systems of Rigid Bodies and Particles

Sample Problem7.2

7.3 Conservation of Energy

Sample Problem 7.3

Problems 7.1-7.45

7.4 Impulse and Momentum

Sample Problem 7.4-7.6

Problems 7.46-7.63

7.5 Eccentric Impact on a Single Rigid Body

Sample Problem 7.7-7.8

Problems 7.64-7.82

7.6 Eccentric Impact

Sample Problem 7.9

Problems 7.83-7.91 

CHAPTER 8 THREE-DIMENSIONAL DYNAMICS OF RIGID BODIES

8.1 Introduction

8.2 Rotational Transformation Between Coordinate Systems

8.2.1 Coordinate Transformations

Sample Problem 8.1-8.2

Problems 8.1-8.10

8.3 Eulerian Angles

8.3.1 Precession of the Equinoxes

Sample Problem 8.3

8.4 Angular Motion

Problems 8.11-8.16

8.5 Joint Coordinate System

Problems 8.17-8.20

8.6 Equations of Motion

Sample Problem 8.4

Problems 8.21-8.31

8.7 Euler's Equations of Motion

8.7.1 Stability of Rotation About a Principal Axis

8.7.2 Motion of an Axisymmetric Object

Sample Problem 8.5

8.7.3 Heavy Axisymmetric Top

8.7.4 Gyroscopic Motion with Steady Precession

8.7.5 Motion of an Axisymmetric Body Subjected to No External Forces

8.7.6 The Gyroscope

Problems 8.32-8.45 

CHAPTER 9 VIBRATION

9.1 Introduction

9.2 Undamped Single-Degree-of-Freedom Systems

9.2.1 Linear Vibration

Sample Problem 9.1-9.2

Sample Problem 9.3

9.2.2 Nonlinear Vibration

Sample Problem 9.4-9.6

Problems 9.1-9.28

9.3 Damped Single-Degree-of-Freedom Systems

9.3.1 Linear Damping

Sample Problem 9.7

Sample Problem 9.8

9.3.2 Nonlinear Damping

Sample Problem 9.9-9.10

Problems 9.29-9.50

9.4 Forced Response and Resonance

9.4.1 Harmonic Excitation of Linear Systems

Sample Problem 9.11

Sample Problem 9.12

Sample Problem 9.13-9.14

9.4.2 General Forced Response

Sample Problem 9.15-9.16

9.4.3 Forced Response of Nonlinear Systems

Sample Problem 9.17-9.18

Problems 9.51-9.85 

APPENDIX A MASS MOMENTS OF INERTIA 

APPENDIX B VECTOR CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS 

DYNAMICS INDEX DICTIONARY 

ANSWEAR TO ODD-NUMBERED PROBLEMS 

INDEX