Spinning Book Movie

From VisualDSolve [Chapter 17: Rigid Bodies]

In this final chapter we examine a very accessible, yet very complicated modeling problem: the rotational motion of a rigid body. In particular, we wish to investigate the apparent instability when an object such as a book is flipped in the air with the cover facing the thrower (i.e., it spins around its medium-length axis).

In fact, the reader should right now get a book, wrap an elastic band around it to keep it closed, and start spinning it. A toss around the smallest of the axes of symmetry (just grab a corner and flick your wrist) yields boring spin: it is very easy to throw and catch the book. And a toss about the longest axis (grab the spine with both hands and spin) likewise yields predictable behavior. But if you hold the book along its bottom edge so that the title faces you, you will find that it is extremely difficult to spin it and catch it after one full turn so that the title faces you. The book, like a talented diver or gymnast, does an extra sideways flip, and lands with its back cover up!

Our goal is to show how the equations can be translated into enlightening animations that illustrate some of the beautiful classical theorems that describe the motion of a rigid body.

Download QuickTime (.mov) or Video for Windows (.avi) movie of spinning book.

Download Mathematica notebook containing code to generate the spinning book movie.

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