Engineering Applications of Dynamics
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Designed to address the perceived failure of introductory dynamics courses to produce students capable of applying dynamic principles successfully, both in subsequent courses and in practice, Engineering Applications of Dynamics adopts a much-needed practical approach designed to make the subject not only more relevant, but more interesting as well.

Written by a highly respected team of authors, the book is the first of its kind to tie dynamics theory directly to real-world situations. By touching on complex concepts only to the extent of illustrating their value in real-world applications, the authors provide students with a deeper understanding of dynamics in the engineering of mechanical systems.

Topics of interest include:
* The formulation of equations in forms suitable for computer simulation
* Simulation examples of real engineering systems
* Applications to vehicle dynamics
* Lagrange's equations as an alternative formulation procedure
* Vibrations of lumped and distributed systems
* Three-dimensional motion of rigid bodies, with emphasis on gyroscopic effects
* Transfer functions for linearized dynamic systems
* Active control of dynamic systems

A Solutions Manual with detailed solutions for al problems in this book is available at the Web site,


Dean C. Karnopp and Donald L. Margolis are professors of mechanical engineering at the University of California, Davis.



Chapter 1: Newton's Laws for Particles and Rigid bodies.

1.1 Newton's 2nd Law.

1.2 Coordinate Frames, Velocity and Acceleration Diagrams.

1.3 Free Body diagrams and Force Diagrams.

1.4 Transferring Velocity and Acceleration Components.

1.5 Transferring Motion Components of Rigid Bodies and Generating Kinematic Constraints.

1.6 Review of Center of Mass, Linear Momentum, and Angular Momentum for Rigid Bodies.

1.7 Newton's law Applied to Rigid Bodies .

1.8 References.

Chapter 2: Equations of Motion in Second and First Order Form.

2.1 Deriving Equations of Motion for Systems of Particles.

2.2 Deriving Equations of Motion When Rigid Bodies are Part of the System.

2.3 Forms of Equations and their Computational Solution.

2.4 Reducing Sets of Second Order Differential Equations to First Order Form.

2.5 Matrix Forms for Linearized Equations.

2.6 Summary.

2.7 References.

Chapter 3: Computer Solution of Equations of Motion.

3.1 Time Step Simulation of Nonlinear Equations of Motion.

3.2 Linear System Response.

3.3 References.

Chapter 4: Energy and Lagrange Equation Methods.

4.1 Kinetic and Potential Energy.

4.2 Using Conservation of Energy to Derive Equations of Motion.

4.3 Equations of Motion from Lagrange's Equations.

4.4 Interpretation of Lagrange's Equations.

4.5 Nonlinear Kinematics and Lagrange's Equations.

4.6 First Order Forms for Lagrange's Equations.

Chapter 5: Newton's Laws in a Body-Fixed Frame: Application to Vehicle Dynamics.

5.1 The Dynamics of a Shopping Cart.

5.2 Analysis of a Simple Car Model.

5.3 Vehicle Stability.

5.4 Stability, Critical Speed, Understeer and Oversteer.

5.5 Steering Transfer Functions.

5.6 Steady Cornering.

5.7 Summary.

5.8 References.

Chapter 6: Mechanical systems under Active Control.

6.1 Basic Concepts.

6.2 State Variables and Active Control.

6.3 Steering Control of Banking Vehicles.

6.4 Active Control of Vehicle Dynamics.

6.5 Summary.

6.6 References.

Chapter 7: Rigid Body Motion in Three Dimensions.

7.1 The General Equations of Motion.

7.2 Use of a Body-Fixed Coordinate Frame.

7.3 Use of an Inertial Coordinate Frame.

7.4 Summary.

7.5 References.

Chapter 8: Vibration of Multiple Degree-Of-Freedom Systems.

8.1 Natural Frequency and Resonance of a One D-O-F Oscillator.

8.2 Two Degree-of-Freedom Systems.

8.3 Tuned Vibration Absorbers.

8.4 Summary.

8.5 References.

Chapter 9: Distributed System Vibrations.

9.1 Stress Waves in a Rod.

9.2 Attaching the Distributed System to External Dynamic Components.

9.3 Tightly Stretched Cable.

9.4 Bernoulli-Euler Beam.

9.5 Summary.

9.6 References.

Appendix 1: Three-Dimensional Rigid Body in a Rotating Coordinate System.

Appendix 2: Moments of Inertia for Some Common Body Shapes.

Appendix 3: The Parallel Axis Theorem.