Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Basic Considerations
- 2 Particle Kinematics
- 3 Relative Motion
- 4 Kinematics of Constrained Rigid Bodies
- 5 Inertial Effects for a Rigid Body
- 6 Newton–Euler Equations of Motion
- 7 Introduction to Analytical Mechanics
- 8 Constrained Generalized Coordinates
- 9 Alternative Formulations
- 10 Gyroscopic Effects
- Appendix
- Answers to Selected Homework Problems
- Index
5 - Inertial Effects for a Rigid Body
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Basic Considerations
- 2 Particle Kinematics
- 3 Relative Motion
- 4 Kinematics of Constrained Rigid Bodies
- 5 Inertial Effects for a Rigid Body
- 6 Newton–Euler Equations of Motion
- 7 Introduction to Analytical Mechanics
- 8 Constrained Generalized Coordinates
- 9 Alternative Formulations
- 10 Gyroscopic Effects
- Appendix
- Answers to Selected Homework Problems
- Index
Summary
Chasle's theorem states that the general motion of a rigid body can be represented as a superposition of a translation following any point in a body and a pure rotation about that point. The kinematics tools we have developed provide the capability to describe these motions in terms of a few parameters. In this chapter we begin to characterize the relationship between forces acting on a rigid body and kinematical parameters for that body. The resultant of a set of forces may be regarded intuitively as the net tendency of the force system to push a body, so one should expect it to be related to the translational effect. Similarly, it is reasonable to expect that the resultant moment of a set of forces represents the rotational influence. We shall confirm and quantify these expectations.
From a philosophical perspective, the shift from statics, in which one equilibrates forces, to kinetics, in which the forces must match an inertial effect, is rather drastic. For a particle, Newton's Second and Third Laws are readily understood in this regard. However, the corresponding shift for the rotational effect will lead to effects associated with the angular momentum of a rigid body that sometimes are counterintuitive. This is especially true for those who try to examine spatial motion from a planar motion viewpoint. This chapter focuses on the determination and evaluation of angular momentum.
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- Engineering Dynamics , pp. 228 - 295Publisher: Cambridge University PressPrint publication year: 2007