The Practice of Engineering Dynamics

Ronald J. Anderson

• Publisher: Wiley
• Year: 2020
• ISBN:
  9781119053699
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

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.

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 – 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

with respect to time is therefore formed from,

1. The rate of change of magnitude
   
   .
2. The rate of change of direction
   
   .

Figure 1.1 A vector changing with time.

Figure 1.1 shows the vector

that changes after a time increment,

, to

.

The difference between

and

can be defined as the vector

shown in Figure 1.1 and, by the rules of vector addition,

(1.1)

or,

(1.2)

Then, using the definition of the time derivative,

(1.3)

Imagine now that Figure 1.1 is compressed to ...