Advanced Engineering Dynamics

H. Harrison, T. Nettleton

• Publisher: Butterworth-Heinemann
• Year: 1997
• ISBN:
  9780080523354
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

'Advanced Engineering Dynamics' bridges the gap between elementary dynamics and advanced specialist applications in engineering.It begins with a reappraisal of Newtonian principles before expanding into analytical dynamics typified by the methods of Lagrange and by Hamilton's Principle and rigid body dynamics. Four distinct vehicle types (satellites, rockets, aircraft and cars) are examined highlighting different aspects of dynamics in each case. Emphasis is placed on impact and one dimensional wave propagation before extending the study into three dimensions. Robotics is then looked at in detail, forging a link between conventional dynamics and the highly specialised and distinctive approach used in robotics. The text finishes with an excursion into the Special Theory of Relativity mainly to define the boundaries of Newtonian Dynamics but also to re-appraise the fundamental definitions. Through its examination of specialist applications highlighting the many different aspects of dynamics this text provides an excellent insight into advanced systems without restricting itself to a particular discipline. The result is essential reading for all those requiring a general understanding of the more advanced aspects of engineering dynamics.

1

Newtonian Mechanics

1.1 Introduction

The purpose of this chapter is to review briefly the assumptions and principles underlying Newtonian mechanics in a form that is generally accepted today. Much of the material to be presented is covered in more elementary texts (Harrison and Nettleton 1994) but in view of the importance of having clear definitions of the terms used in dynamics all such terms will be reviewed.

Many of the terms used in mechanics are used in everyday speech so that misconceptions can easily arise. The concept of force is one that causes misunderstanding even among those with some knowledge of mechanics. The question as to whether force is the servant or the master of mechanics often lies at the root of any difficulties. We shall consider force to be a useful servant employed to provide communication between the various aspects of physics. The newer ideas of relativity and quantum mechanics demand that all definitions are reappraised; however, our definitions in Newtonian mechanics must be precise so that any modification required will be apparent. Any new theory must give the same results, to within experimental accuracy, as the Newtonian theory when dealing with macroscopic bodies moving at speeds which are slow relative to that of light. This is because the degree of confidence in Newtonian mechanics is of a very high order based on centuries of experiment.

1.2 Fundamentals

The earliest recorded writings on the subject of mechanics are those of Aristotle and Archimedes some two thousand years ago. Although some knowledge of the principles of levers was known then there was no clear concept of dynamics. The main problem was that it was firmly held that the natural state of a body was that of rest and therefore any motion required the intervention of some agency at all times. It was not until the sixteenth century that it was suggested that straight line steady motion might be a natural state as well as rest. The accurate measurement of the motion of the planets by Tycho Brahe led Kepler to enunciate his three laws of planetary motion in the early part of the seventeenth century. Galileo added another important contribution to the devel...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Chapter 1: Newtonian Mechanics
• Chapter 2: Lagrange’s Equations
• Chapter 3: Hamilton’s Principle
• Chapter 4: Rigid Body Motion in Three Dimensions
• Chapter 5: Dynamics of Vehicles
• Chapter 6: Impact and One-Dimensional Wave Propagation
• Chapter 7: Waves In a Three-Dimensional Elastic Solid
• Chapter 8: Robot Arm Dynamics
• Chapter 9: Relativity
• Problems
• Appendix 1: Vectors, Tensors and Matrices
• Appendix 2: ANALYTICAL DYNAMICS
• Appendix 3: Curvilinear co-ordinate systems
• Bibliography
• Index