The Practice of Engineering Dynamics
eBook - ePub

The Practice of Engineering Dynamics

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

The Practice of Engineering Dynamics

About this book

The Practice of Engineering Dynamics is a textbook that takes a systematic approach to understanding dynamic analysis of mechanical systems. It comprehensively covers dynamic analysis of systems from equilibrium states to non-linear simulations and presents frequency analysis of experimental data. It divides the practice of engineering dynamics into three parts: Part 1 - Modelling: Deriving Equations of Motion; Part 2 - Simulation: Using the Equations of Motion; and Part 3- Experimental Frequency Domain Analysis. This approach fulfils the need to be able to derive the equations governing the motion of a system, to then use the equations to provide useful design information, and finally to be able to analyze experimental data measured on dynamic systems.

The Practice of Engineering Dynamics includes end of chapter exercises and is accompanied by a website hosting a solutions manual.

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Part I
Modeling: Deriving Equations of Motion

1
Kinematics

Kinematics is defined as the study of motion without reference to the forces that cause the motion. A proper kinematic analysis is an essential first step in any dynamics problem. This is where the analyst defines the degrees of freedom and develops expressions for the absolute velocities and accelerations of the bodies in the system that satisfy all of the physical constraints. The ability to differentiate vectors with respect to time is a critical skill in kinematic analysis.

1.1 Derivatives of Vectors

Vectors have two distinct properties โ€“ magnitude and direction. Either or both of these properties may change with time and the time derivative of a vector must account for both.
The rate of change of a vector
images
with respect to time is therefore formed from,
  1. The rate of change of magnitude
    images
    .
  2. The rate of change of direction
    images
    .
Schematic illustration of a vector changing with time.
Figure 1.1 A vector changing with time.
Figure 1.1 shows the vector
images
that changes after a time increment,
images
, to
images
.
The difference between
images
and
images
can be defined as the vector
images
shown in Figure 1.1 and, by the rules of vector addition,
(1.1)
equation
or,
(1.2)
equation
Then, using the definition of the time derivative,
(1.3)
equation
Imagine now that Figure 1.1 is compressed to ...

Table of contents

  1. Cover
  2. Table of Contents
  3. Preface
  4. About the Companion Website
  5. Part I: Modeling: Deriving Equations of Motion
  6. Part II: Simulation: Using the Equations of Motion
  7. Part III: Working with Experimental Data
  8. A Representative Dynamic Systems
  9. B Moments and Products of Inertia
  10. C Dimensions and Units
  11. D Least Squares Curve Fitting
  12. Index
  13. End User License Agreement