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abstract: 'A rattleback is a rigid, semi-elliptic toy which exhibits unintuitive behavior; when it is spun in one direction, it soon begins pitching and stops spinning, then it starts to spin in the opposite direction, but in the other direction, it seems to spin just steadily. This puzzling behavior results from the slight misalignment between the principal axes for the inertia and those for the curvature; the misalignment couples the spinning with the pitching and the rolling oscillations. It has been shown that under the no-slip condition and without dissipation the spin can reverse in both directions, and Garcia and Hubbard obtained the formula for the time required for the spin reversal $t_r$ \[Proc. R. Soc. Lond. A **418**, 165 (1988)\]. In this work, we reformulate the rattleback dynamics in a physically transparent way and reduce it to a three-variable dynamics for spinning, pitching, and rolling. We obtain an expression of the Garcia-Hubbard formula for $t_r$ by a simple product of four factors: (1) the misalignment angle, (2) the difference in the inverses of inertia moment for the two oscillations, (3) that in the radii for the two principal curvatures, and (4) the squared frequency of the oscillation. We 