Geometric Origin of the Tennis Racket Effect

Abstract

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the Monster flip, an almost impossible skate board trick.

25 pages, 12 figures

References in corpus (2)

• The tennis racket effect in a three-dimensional rigid body
• Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy

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