Page 260 - Dynamics of Mechanical Systems

0593_C08_fm Page 241 Monday, May 6, 2002 2:45 PM

8

Principles of Dynamics: Newton’s Laws

and d’Alembert’s Principle

8.1 Introduction
Dynamics is a combined study of motion (kinematics), forces (kinetics), and inertia (mass
distributing). By using the principles of dynamics we can obtain mathematical models of
the behavior of mechanical systems. In this chapter, and in subsequent chapters, we will
explore the principles of dynamics and their applications.
The development of dynamics principles dates back to at least the 14th century, long
before the development of calculus and other widely used analytical procedures. One of
the earliest statements of a dynamics principle in the Western world is attributed to John
Buridan in (1358) [8.1]:

From this theory also appears the cause of why the natural motion of a heavy body
downward is continually accelerated. For from the beginning only the gravity was
moving it. Therefore, it moved more slowly, but in moving it impressed in the heavy
body an impetus. This impetus now together with its gravity moves it. Therefore, the
motion becomes faster, and by the amount it is faster so the impetus becomes more
intense. Therefore, the movement evidently becomes continually faster.
While this statement seems to be intuitively reasonable, it is not strictly correct, as we
now understand the physics of falling bodies. Moreover, the statement does not readily
lead to a quantitative analysis.
The earliest principles that adequately describe the physics and lead to quantitative
analysis are generally attributed to Isaac Newton. His principles, first published in 1687,
are generally stated in three laws [8.2]:

First law (law of inertia): In the absence of forces applied to a particle, the particle
will remain at rest or it will move along a straight line at constant velocity.
Second law (law of kinetics): If a force is applied to a particle, the particle accelerates
in the direction of the force. The magnitude of the acceleration is proportional
to the magnitude of the force and inversely proportional to the mass of the
particle.
Third law (law of action–reaction): If two particles exert forces on each other, the
respective forces are equal in magnitude and oppositely directed along the line
joining the particles.

241