1
C H A P T E R 1
Introduction
1.1 BACKGROUND AND MOTIVATION
Engineering dynamics is an extremely interesting subject and is rich in topics that are impor-
tant to the solution of everyday problems encountered in the design and analysis in engineering.
ere are many interesting examples in the conceptual and physical worlds. In this chapter only
four classical examples are presented to illustrate the interesting and useful aspects of engineer-
ing dynamics. ese examples, while regarded as classical (non-quantum), have many relevant
modern applications and important results that remain to be explored and deep understanding
to be made. In the following sections these examples are to be included accordingly.
1.1.1 CLASSICAL WATER MOLECULE AND OZONE MOLECULE
e water molecule is composed of three particles interacting by interparticle conservative forces,
as illustrated in Figure 1.1 in which m
o
is the mass of the oxygen atom and m the mass of the
hydrogen atom. When m
o
D m, the system becomes the ozone molecule that is of great interest
to environmental engineers and scientists. e water molecule is of course the classical three-body
problem in space [1, 2]. It is a special case of the n-body problem. For the three-body problem
there is no general closed-form solution for every condition.
Y
X
Z
O
m
o
r⃑
o
r⃑
2
r⃑
1
m
m
Figure 1.1: Water molecule in 3D space.
Historically, the first specific three-body problem that received extended study was that
dealt with the Moon, the Earth, and the Sun [1]. e gravitational problem of three bodies in
space dates from 1687, when Newton [3] published his famous Principia.
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