When ______, it is straightforward to show that _____, which means that the ball undergoes simple rolling at the point of contact after the first bounce. Thus for _______, Eq. (15) indicates that the ball undergoes a transition to simple rolling as _____. Figure 2(b) shows this transition for the initial conditions used in Fig 2(a). This transition captures an aspect of superball motion that many find very useful; it is much easier to pick up a dropped ball if you wait until the erratic bouncing decays to simple rolling.
Finally, consider the eigenvalues and eigenvectors of M The first eigenvalue for this matrix is ______ and the corresponding eigenvector is