The Practice of Engineering Dynamics

Cover
Title Page
Copyright
Contents
Preface
About the Companion Website
Part I Modeling: Deriving Equations of Motion
Chapter 1 Kinematics
	1.1 Derivatives of Vectors
	1.2 Performing Kinematic Analysis
	1.3 Two Dimensional Motion with Constant Length
	1.4 Two Dimensional Motion with Variable Length
	1.5 Three Dimensional Kinematics
	1.6 Absolute Angular Velocity and Acceleration
	1.7 The General Acceleration Expression
	Exercises
Chapter 2 Newton's Equations of Motion
	2.1 The Study of Motion
	2.2 Newton's Laws
	2.3 Newton's Second Law for a Particle
	2.4 Deriving Equations of Motion for Particles
	2.5 Working with Rigid Bodies
	2.6 Using F→=ma→ in the Rigid Body Force Balance
	2.7 Using F→=dG→dt in the Rigid Body Force Balance
	2.8 Moment Balance for a Rigid Body
	2.9 The Angular Momentum Vector – H→O
	2.10 A Physical Interpretation of Moments and Products of Inertia
	2.11 Euler's Moment Equations
	2.12 Throwing a Spiral
	2.13 A Two Body System
	2.14 Gyroscopic Motion
	Exercises
Chapter 3 Lagrange's Equations of Motion
	3.1 An Example to Start
	3.2 Lagrange's Equation for a Single Particle
	3.3 Generalized Forces
	3.4 Generalized Forces as Derivatives of Potential Energy
	3.5 Dampers – Rayleigh's Dissipation Function
	3.6 Kinetic Energy of a Free Rigid Body
	3.7 A Two Dimensional Example using Lagrange's Equation
		3.7.1 The Kinetic Energy
		3.7.2 The Potential Energy
		3.7.3 The θ Equation
		3.7.4 The ϕ Equation
	3.8 Standard Form of the Equations of Motion
	Exercises
Part II Simulation: Using the Equations of Motion
Chapter 4 Equilibrium Solutions
	4.1 The Simple Pendulum
	4.2 Equilibrium with Two Degrees of Freedom
	4.3 Equilibrium with Steady Motion
	4.4 The General Equilibrium Solution
	Exercises
Chapter 5 Stability
	5.1 Analytical Stability
	5.2 Linearization of Functions
	5.3 Example: A System with Two Degrees of Freedom
	5.4 Routh Stability Criterion
	5.5 Standard Procedure for Stability Analysis
	Exercises
Chapter 6 Mode Shapes
	6.1 Eigenvectors
	6.2 Comparing Translational and Rotational Degrees of Freedom
	6.3 Nodal Points in Mode Shapes
	6.4 Mode Shapes with Damping
	6.5 Modal Damping
	Exercises
Chapter 7 Frequency Domain Analysis
	7.1 Modeling Frequency Response
	7.2 Seismic Disturbances
	7.3 Power Spectral Density
		7.3.1 Units of the PSD
		7.3.2 Simulation using the PSD
	Exercises
Chapter 8 Time Domain Solutions
	8.1 Getting the Equations of Motion Ready for Time Domain Simulation
	8.2 A Time Domain Example
	8.3 Numerical Schemes for Solving the Equations of Motion
	8.4 Euler Integration
	8.5 An Example Using the Euler Integrator
	8.6 The Central Difference Method: An O(h2) Method
	8.7 Variable Time Step Methods
	8.8 Methods with Higher Order Truncation Error
	8.9 The Structure of a Simulation Program
	Exercises
Part III Working with Experimental Data
Chapter 9 Experimental Data – Frequency Domain Analysis
	9.1 Typical Test Data
	9.2 Transforming to the Frequency Domain – The CFT
	9.3 Transforming to the Frequency Domain – The DFT
	9.4 Transforming to the Frequency Domain – A Faster DFT
	9.5 Transforming to the Frequency Domain – The FFT
	9.6 Transforming to the Frequency Domain – An Example
	9.7 Sampling and Aliasing
	9.8 Leakage and Windowing
	9.9 Decimating Data
	9.10 Averaging DFTs
	Exercises
A Representative Dynamic Systems
	A.1 System 1
	A.2 System 2
	A.3 System 3
	A.4 System 4
	A.5 System 5
	A.6 System 6
	A.7 System 7
	A.8 System 8
	A.9 System 9
	A.10 System 10
	A.11 System 11
	A.12 System 12
	A.13 System 13
	A.14 System 14
	A.15 System 15
	A.16 System 16
	A.17 System 17
	A.18 System 18
	A.19 System 19
	A.20 System 20
	A.21 System 21
	A.22 System 22
	A.23 System 23
B Moments and Products of Inertia
	B.1 Moments of Inertia
	B.2 Parallel Axis Theorem for Moments of Inertia
	B.3 Parallel Axis Theorem for Products of Inertia
	B.4 Moments of Inertia for Commonly Encountered Bodies
C Dimensions and Units
D Least Squares Curve Fitting
Index
EULA