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 10: Gyroscopic Effects
The focus thus far has been on the derivation of equations of motion for rigid-body motion. Sometimes the goal was to characterize the force system required to produce a specified motion, while other situations entailed where the response was not known, which led to differential equations of motion. Both situations will be encountered in this chapter, where the common thread is the prominent role of gyroscopic action. Such phenomena are exploited in gyroscopes, whose theory will be introduced here. However, much can be learned about the nature of dynamical responses by beginning with studies of simpler, yet more common, systems that display similar effects.
10.1 FREE MOTION
One of the first types of spatial motion treated in basic physics and engineering courses on mechanics is projectile motion, whose study is devoted to the determination of the motion of the center of mass. In contrast, the manner in which the body rotates about its center of mass is seldom discussed in a fundamental course. Our study of free rotation will be based on the assumption that the only external force is gravitational attraction acting at the center of mass. The corollary is that the resultant moment about the center of mass is zero, from which it follows that
A further corollary of taking the resultant moment to be zero is that the rotational motion occurs independently of the motion of the center of mass. In reality, aerodynamic forces acting on a body may be represented as a force couple system acting at...
Copyright Jerry Ginsberg 2008 under license agreement with Books24x7
