Engineering Dynamics
With numerous examples implementing a consistent pedagogical structure, this thorough guide provides a modern vector-oriented treatment of classical dynamics and its application to engineering problems.
TABLE OF CONTENTS Engineering Dynamics
Chapter 3: Relative Motion
When we ride in an automobile or airplane, the reference frame for our observations is moving. If we wish to use such observations to formulate Newton s Laws, we need to convert them to an inertial reference frame. More fundamentally, the basic fact that the points in a moving rigid body are stationary as viewed from that body is a vital aspect. In this chapter we develop the ability to correlate observations of position, velocity, and acceleration from fixed and moving reference frames.
3.1 COORDINATE TRANSFORMATIONS
It is standard terminology to refer to any quantity that is measured relative to a fixed reference frame as absolute, whereas quantities measured with respect to any moving reference frame are relative. Figure 3.1 depicts a general situation in which point P is being observed from a moving reference frame xyz whose motion we presumably know, whereas XYZ is a fixed reference frame. It is apparent from Fig. 3.1 that one can arrive at the absolute position r P/O by proceeding first to the xyz origin along 
, then following the relative position 
, so that
Despite the simple appearance of this relation, it embodies many of the issues that we generally encounter. Both r P/O and describe position as seen from a specific reference frame. Each vector could be represented in terms of components relative to the coordinate axes of its associated reference frame. However, if we are to evaluate the sum by adding like components,...
Copyright Jerry Ginsberg 2008 under license agreement with Books24x7
