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RESEARCH PRODUCT
Geometric Origin of the Tennis Racket Effect
G. J. Gutierrez GuillenL. Van DammePavao MardešićDominique Sugnysubject
Physics[PHYS]Physics [physics]Riemann surfaceGeneral Physics and AstronomyClassical Physics (physics.class-ph)FOS: Physical sciencesMathematical Physics (math-ph)Physics - Classical PhysicsRigid body01 natural sciencesUpper and lower boundssymbols.namesakePerpendicular AxisClassical mechanics[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Phase space0103 physical sciencesRacketsymbolsIdeal (ring theory)Twist010306 general physicscomputerMathematical Physicscomputer.programming_languagedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-08-06 |