Essentials of Dynamics and Vibrations

  • John Billingsley

Table of contents

  1. Front Matter
    Pages i-vii
  2. John Billingsley
    Pages 1-11
  3. John Billingsley
    Pages 13-21
  4. John Billingsley
    Pages 23-29
  5. John Billingsley
    Pages 31-56
  6. John Billingsley
    Pages 57-61
  7. John Billingsley
    Pages 63-67
  8. John Billingsley
    Pages 69-73
  9. John Billingsley
    Pages 75-82
  10. John Billingsley
    Pages 83-94
  11. John Billingsley
    Pages 95-98
  12. John Billingsley
    Pages 99-119
  13. John Billingsley
    Pages 121-137
  14. John Billingsley
    Pages 139-144
  15. Back Matter
    Pages 145-165

About this book


Dynamic objects move in mysterious ways. Their analysis is a difficult subject involving matrices, differential equations and the complex algebra of oscillatory systems. However, in this textbook, the author draws on his long experience of designing autopilots, robots for nuclear inspection and agricultural machine guidance to present the essentials with a light touch. The emphasis is on a deep understanding of the fundamentals rather than rote-learning of techniques. The inertia tensor is presented as a key to understanding motion ranging from boomerangs to gyroscopes. Chains of transformations unravel the motion of a robot arm.

To help the reader visualise motion, ranging from unbalanced rotors to vibrating systems with multiple modes and damping, there are abundant simulation examples on a linked website. These will run in any web browser, while their simple code is on open view for modification and experimentation. They show that nonlinear systems present no problems, so that friction damping can be modelled with ease. 

A particular problem for mechanical engineers is that the vibration topics encroach on the territory of the electrical engineer. State variables open up control theory while the solution of differential equations with sinusoidal inputs is simplified by an understanding of sine-waves as complex exponentials. The linked web site has several areas of mathematics revision to help. 

A final chapter pokes fun at the misrepresentation of dynamics in cinema productions. 


Solid body dynamics Three Dimensional Kinematics Differential equations Nonlinear Systems Inertia tensor

Authors and affiliations

  • John Billingsley
    • 1
  1. 1.Faculty of Health, Engineering and ScienceUniversity of Southern QueenslandToowoombaAustralia

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-56516-3
  • Online ISBN 978-3-319-56517-0
  • Buy this book on publisher's site