Introduction and Fundamentals
Introduction
Short History of Dynamics
Units
Planar Kinematics of Particles
Introduction
Motion in a Straight Line
Particle Motion in a Plane: Cartesian Coordinates
Coordinate Transformations: Relationships between Components of a Vector in Two-Coordinate Systems
Particle Motion in a Plane: Polar Coordinates
Particle Motion in a Plane: Normal-Tangential (Path) Coordinates
Moving between Cartesian, Polar-, and Path-Coordinate Definitions for Velocity and Acceleration Components
Time-Derivative Relationships in Two-Coordinate Systems
Velocity and Acceleration Relationships in Two Cartesian Coordinate Systems
Relative Position, Velocity, and Acceleration Vectors between Two Points in the Same Coordinate System
Summary and Discussion
Problems
Planar Kinetics of Particles
Introduction
Differential Equations of Motion for a Particle Moving in a Straight Line: An Introduction to Physical Modeling
More Motion in a Straight Line: Degrees of Freedom and Equations of Kinematic Constraints
Motion in a Plane: Equations of Motion and Forces of Constraint
Particle Kinetics Examples with More than 1DOF
Work-Energy Applications for 1DOF Problems in Plane Motion
Linear-Momentum Applications in Plane Motion
Moment of Momentum
Summary and Discussion
Problems
Planar Kinematics of Rigid Bodies
Introduction
Rotation about a Fixed Axis
Velocity and Acceleration Relationships for Two Points in a Rigid Body
Rolling without Slipping
Planar Mechanisms
Summary and Discussion
Problems
Planar Kinetics of Rigid Bodies
Introduction
Inertia Properties and the Parallel-Axis Formula
Governing Force and Moment Equations for a Rigid Body
Kinetic Energy for Planar Motion of a Rigid Body
Fixed-Axis-Rotation Applications of the Force, Moment, and Energy Equations
Compound Pendulum Applications
General Applications of Force, Moment, and Energy Equations for Planar Motion of a Rigid Body
Moment of Momentum for Planar Motion
Summary and Discussion
Problems
Lagrange’s Equations of Motion
Introduction
Deriving Lagrange’s Equations of Motion
Applying Lagrange’s Equation of Motion to Problems without Kinematic Constraints
Conservation of Momenta from Lagrange’s Equations of Motion
Application of Lagrange’s Equations to Examples with Algebraic Kinematic Constraints
Using Lagrange Multipliers to Define Reaction Forces for Systems with Generalized Coordinates
Summary and Discussion
Problems
A: Essentials of Matrix Algebra
B: Essentials of Differential Equations
Mass Properties of Common Solid Bodies
Answers to Selected Problems
References
Biography
Dr. Dara Childs is professor of mechanical engineering at Texas A&M University (TAMU) in College Station, Texas. He has been director of the TAMU Turbomachinery Laboratory since 1984. He has received several best-paper awards, is an American Society of Mechanical Engineers (ASME) life fellow, and received the ASME Henry R. Worthington medal for outstanding contributions in pumping machinery. He is the author of many conference and journal papers plus two prior books. Dr. Childs has taught graduate and undergraduate courses in dynamics and vibrations since 1968: Colorado State University (1968–1971), University of Louisville (1971–1980), TAMU (1980–present).
Andrew P. Conkey
received his PhD from Texas A&M University (TAMU) in 2007, where his research was in the application of the fiber Fabry–Perot interferometer to machinery/vibration measurements. He received his bachelor’s and master’s degrees from TAMU–Kingsville. He has over 16 years of teaching experience, having taught at TAMU–Kingsville, TAMU–College Station, TAMU–Qatar, and TAMU–Corpus Christi. In addition to teaching, he has worked for a refinery, a fiber-optic sensor company, and an engineering consulting firm."It is easy to identify students who learned dynamics from (previous editions) of this book…. They are confident, they approach new problems based on fundamental principles, they are not afraid of dynamics. The integrated, differential equations & fundamental principles based approach removes the dread from dynamics! No longer is there fear an uncertainty of picking the correct equation & guessing the correct special case… every problem can be methodically approached from the same few principles and conquered."
—James R Morgan, Charles Sturt University, Bathurst, NSW, Australia
