Applied Dynamics  book cover
1st Edition

Applied Dynamics

ISBN 9781482250732
Published December 12, 2014 by CRC Press
876 Pages 643 B/W Illustrations

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Book Description

Gain a Greater Understanding of How Key Components Work

Using realistic examples from everyday life, including sports (motion of balls in air or during impact) and vehicle motions, Applied Dynamics emphasizes the applications of dynamics in engineering without sacrificing the fundamentals or rigor. The text provides a detailed analysis of the principles of dynamics and vehicle motions analysis. An example included in the topic of collisions is the famous "Immaculate Reception," whose 40th anniversary was recently celebrated by the Pittsburgh Steelers.

Covers Stability and Response Analysis in Depth

The book addresses two- and three-dimensional Newtonian mechanics, it covers analytical mechanics, and describes Lagrange’s and Kane’s equations. It also examines stability and response analysis, and vibrations of dynamical systems. In addition, the text highlights a developing interest in the industry—the dynamics and stability of land vehicles.

Contains Lots of Illustrative Examples

In addition to the detailed coverage of dynamics applications, over 180 examples and nearly 600 problems richly illustrate the concepts developed in the text.

Topics covered include:

  • General kinematics and kinetics
  • Expanded study of two- and three-dimensional motion, as well as of impact dynamics
  • Analytical mechanics, including Lagrange’s and Kane’s equations
  • The stability and response of dynamical systems, including vibration analysis
  • Dynamics and stability of ground vehicles

Designed for classroom instruction appealing to undergraduate and graduate students taking intermediate and advanced dynamics courses, as well as vibration study and analysis of land vehicles, Applied Dynamics can also be used as an up-to-date reference in engineering dynamics for researchers and professional engineers.

Table of Contents

Introductory Concepts


Particles, Rigid Bodies and Deformable Solids

Degrees of Freedom

Types of Forces and Motions

Systems of Units


Differential Equations and the Principle of Superposition

Dimensional Analysis and Nondimensionalization

Numerical Integration

What Is a Vehicle?

Cause and Effect Principle



Kinematics Fundamentals


Position, Velocity and Acceleration

Reference Frames: Single Rotation in a Plane

Column Vector Representation

Commonly Used Coordinate Systems

Moving Reference Frames

Selection of Rotation Parameters

Rate of Change of a Vector, Angular Velocity

Angular Acceleration and Second Derivatives

Relative Motion

Instantaneous Center of Zero Velocity



Kinematics Applications


Motion with Respect to the Rotating Earth



Bicycle Model of a Car

Kinematic Differential Equations

Topspin and Backspin


Instant Center Analysis for Linkages



Kinetics Fundamentals


Rigid Body Geometry

Linear and Angular Momentum

Resultant Force and Moment

Laws of Motion

Forces and Moments Acting on Bodies

Force of Gravity

Contact and Reaction Forces

Dry Friction Forces

Aerodynamic Forces

Spring Forces




Kinetics Applications



Mechanical Trail

Impulse and Momentum

Work, Energy and Power

Equations of Motion

Solution of the Equations of Motion

Linearization, Equilibrium and Stability

Motion in the Vicinity of the Earth


A More Accurate Model of Rigid Body Impact



Response of Dynamical Systems


The Unit Impulse and Unit Step Functions

Homogeneous Plus Particular Solution Approach

Laplace Transform Solution

Response of First-Order Systems

Review of Complex Variables

Second-Order Systems

Free Response of Undamped Second-Order Systems

Free Response of Damped Second-Order Systems

Underdamped Systems

Damping Estimation by Logarithmic Decrement

Response to an Impulsive Force

Step Response

Response to General Excitations ‒ Convolution Integral

Time-Domain vs. Frequency-Domain Analysis

Response to Harmonic Excitation


Transmitted Force

Base Excitation

Harmonic Excitation Due to Imbalances and Eccentricity



Response of Multi Degree of Freedom Systems


Modeling of Multi Degree of Freedom Systems


Free Motion of Undamped Multi Degree of Freedom Systems

Solving for the Natural Frequencies and Modal Vectors

Beat Phenomenon

Unrestrained Motion and Rigid Body Modes

Orthogonality of the Modal Vectors

Expansion Theorem

Modal Equations of Motion and Response

Mode Participation and Isolation

Approximate Approach for Damped Systems

Response to Harmonic Excitation

Vibration Reducing Devices

First-Order Systems

Numerical Integration



Analytical Mechanics


Generalized Coordinates and Constraints

Velocity Representation

Virtual Displacements and Virtual Work

Virtual Displacements and Virtual Work for Rigid Bodies

Generalized Forces

Principle of Virtual Work for Static Equilibrium

D'Alembert's Principle

Hamilton's Principle

Lagrange's Equations

Constrained Systems

Kane's Equations

Natural and Nonnatural Systems, Equilibrium

Small Motions around Equilibrium

Rayleigh's Dissipation Function

Generalized Momentum, First Integrals

Impulsive Motion



Three-Dimensional Kinematics of Rigid Bodies


Basic Kinematics of Rigid Bodies

Euler Angles

Axisymmetric Bodies


Orientation Change by Successive Rotations


Matrix Description of a General Transformation

Euler Parameters

Rodrigues Parameters



Mass Moments of Inertia


Center of Mass

Mass Moment of Inertia

Calculation of the Mass Moments and Products of Inertia

Transformation Properties of the Inertia Matrix

Principal Moments of Inertia



Dynamics of Three-Dimensional Rigid Body Motion


Linear and Angular Momentum

Transformation Properties of Angular Momentum

General Describing Equations

Description in Terms of Body-Fixed Coordinates

Angular Momentum Balance for Axisymmetric Bodies

Stability Analysis of Rotational Motion

Steady Precession of a Rolling Disk

Rotation about a Fixed Axis

Impulse and Momentum

Energy and Work

Analytical Equations for Rigid Bodies

Torque-Free Motion of Axisymmetric Bodies



Vehicle Dynamics ‒ Basic Loads and Longitudinal Motions


Vehicle Coordinate Systems and Nomenclature

Loads on Vehicles



More Advanced Model Including Wheel Inertia


Rollover and Lateral Instability

Weight Shift and Statical Indeterminacy



Vehicle Dynamics ‒ Tire and Aerodynamic Forces



Tire Forces

Lateral Forces and Tire Slip

Tire Torques

Slip Ratio and Longitudinal Tire Forces

Rolling Resistance


Other Tire Effects

Summary of Tire Force Effects

Nondimensional Analysis of Tire Behavior

Aerodynamic Forces



Vehicle Dynamics ‒ Lateral Stability


Kinematics ‒ Steer Angle Definitions

Wheel Loads and Slip Angles

Slip Angle Kinematics

Transient Motion Equations


Eigenvalue Analysis

Mass-Spring-Damper Analogy

Steady-State Response

Yaw Velocity Gain and Curvature Response

Tangent Speed and Hydroplaning

Neutral Steer Point

Driver Models

Electronic Stability Control

Which Wheels Will Slide First?



Vehicle Dynamics ‒ Bounce, Pitch and Roll


Sources of Excitation

Unsprung vs. Sprung Mass

Simple Suspension Models

Quarter-Car Model

Pitch and Bounce Motions

Olley Criteria

Response to Harmonic Excitation

Roll Dynamics

Roll Center Analysis

Lateral Force Reduction due to Weight Shift

Roll Axis

Introduction to Suspension Systems

Suspension System Terminology and Geometry

Axle Suspensions

Independent Suspensions

Roll Center Construction



Anti-Roll Bar

Force Analysis for Anti-Squat and Anti-Dive





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Haim Baruh has over 30 years’ experience in teaching and research associated with motion analysis and its applications, such as vibrations, control general dynamics, impact mechanics, and vehicle dynamics. Author of over 40 peer-reviewed research articles, as well as the highly-regarded book, Analytical Dynamics, and director of a NASA-funded successful STEM education center, Baruh’s educational and research efforts have been supported by NASA, NSF, and the FAA. He has collaborated on research with the U.S. Army and he has served as graduate program director and associate dean in the School of Engineering at Rutgers, the State University of New Jersey.


"The book is a classical and detailed introduction to applied engineering dynamics and it is also a nice treatise on the analytical mechanics—holonomic and nonholonomic mechanical systems, especially kinematics and dynamics of the rigid bodies and vehicle dynamics. … useful tool for undergraduate and graduate students, professors, and researchers in the area of theoretical and applied mechanics and mechanical engineering. … a valuable addition to this field and probably will serve as a reference for a long time."
Journal of Geometry and Symmetry in Physics, 39, 2015

"Overall, this is an excellent book and highly recommended. The coverage of the topics is wide-ranging, which makes it suitable for both undergraduate and graduate courses on dynamics. What makes this book truly different from the rest are the applications of the dynamics principles to real-world systems, such as vibrating systems and vehicles."
—Ilhan Tuzcu, California State University, Sacramento, USA

"The combination of applications with theory without compromising either one is excellently done! Also, the unified and fresh approach to dynamics is excellent. …This book is like a breath of fresh air…"
—Sorin Siegler, Drexel University, Philadelphia, Pennsylvania, USA

"This text has a thorough coverage of both introductory and advanced topics in dynamics while focusing on topics useful for solving practical problems, including many associated with the design of ground-based vehicles."
—James W. Kamman, Western Michigan University

"The book presentation is very practical and the text flows nicely. Easy to read with a physically pleasing layout of text and figures. I really appreciate the appearance of the text!!!! --- after all, this is an ENGINEERING book!!!! The numerous examples are very helpful to the student."
—Robert M. Sexton, Associate Professor, Virginia Commonwealth University