JB  1st ed   2nd edition 

Essentials of Dynamics and Vibration

Look out for the second edition!

By John Billingsley   Published by Springer

First edition simulations

About the first edition

After all the proofreading, some errors are sure to remain.  If you spot an error, please email me to point it out!  To defeat the spammers, replace the name 'junk' in junk@essdyn.com with 'john'.

I hope that you have noticed that there is something a bit different about this book.  Effort has been made to keep the main material as simple as possible.  The main effort has been to give a fundamental understanding, so that you can work out your own way to tackle problems that you have never met before.

Some other books embroider their exercises with pulleys and slopes, piling on example after example until you have learned the techniques by rote.  But dynamics, and engineering in general, is not about numerical agility to stuff numbers into formulae.  It is about understanding how things move, with the ability to choose the right mathematical tool to do the job in question.

So from time to time examples might be posted here that have been used as questions in a 'closed book' examination where no calculators are permitted at all.

Maybe you can suggest changes you would like to see in a future edition.

Best wishes

John

Second edition simulations

About the second edition

In the first edition, the aim was to make this incredibly difficult subject as understandable as possible. But on revising it, it became clear that explanations could be improved. The three-dimensional motion of a solid object can be surprising, and more dynamic simulations have been added to explain it. These can be found on this website but you will also find a way to copy them to your own machine for offline use. Folllow the instructions at the start of the book.

Those simulations will run as web pages in any browser. They range from robot arms and unbalanced spinning rotors, to vibrating systems with multiple modes and damping. They include physical experiments that you can try yourself, such as ‘Newton’s Cradle’, ‘Galilean Cannon’, gyroscopes and boomerangs. Thereis an example of the ‘Dancing T-handle in zero-g’, a video that can be found with an internet search.

These all help the digestion of matrices, tensors, transformations, eigenvectors and functions of a complex variable. The topics are here given a light touch, to assist a deep understanding, while a plentiful supply of exercises and their solutions can help students test that understanding.

Two final chapters apply an even lighter touch, to probe deep misconceptions about Black Holes, energy and the wild imagination of the film industry. Jules Verne suffers from close inspection.
If the energy to heat your bath-water were instead used to lift it into the air, how high would it get? What is the maximum power that you could harvest by putting piezo transducers under paving slabs?