If you try to spin a tennis racket (or a book, etc.) around any of its three principal axes, you will find that different things happen with the different axes. Assuming that the principal moments (relative to the CM) are labeled according to I1 > I2 > I3 (see Fig.), you will find that the racket will spin nicely around the x1 and x3 axes, but it will wobble in a rather messy manner if you try to spin it around the x2 axis. Verify this claim experimentally with a book (preferably lightweight, and wrapped with a rubber band), or a tennis racket (if you happen to study with one on hand). Verify this claim mathematically. The main point here is that you can??t start the motion off with ? pointing exactly along a principal axis. Therefore, what you want to show is that the motion around the x1 and x3 axes is stable (that is, small errors in the initial conditions remain small); whereas the motion around the x2 axis is unstable (that is, small errors in the initial conditions get larger and larger, until the motion eventually doesn??t resemble rotation around the x2 axis).23 Your task is to use Euler??s equations to prove these statements about stability. (Exercise 3 gives another derivation of this result.)

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X3 X2