Dzhanibekov Effect
Dzhanibekov Effect
This Demonstration illustrates the Dzhanibekov effect, discovered on a Russian space station in 1985. Later on it was rediscovered as an unexpected behavior of a tennis racket flipped into the air. When ≈/2 for the kinetic energy of an asymmetric top, the top can exhibit periodic flipping. Here is the angular momentum and is the intermediate moment of inertia. In this Demonstration, the moments of inertia are chosen to be 1, 2, 3, and the magnitude of the angular momentum vector is normalized to 1. Flipping occurs when the kinetic energy is very close to 0.25. When is exactly equal to 0.25, there is just one flip, here around . The simulation is based on exact solutions of the Euler and Arnold equations for the angular momentum and the attitude matrix, using Mathematica's built-in elliptic functions JacobiSN, JacobiCN, JacobiDN, JacobiAmplitude and EllipticPi.
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t=0