Behavior of a falling paper in a two-dimensional fluid is investigated by introducing a simple phenomenological model including the lift and friction terms. Five falling patterns are discovered with the increase of friction coefficients: periodic rotation, chaotic rotation, chaotic fluttering, periodic fluttering, and simple perpendicular fall. Irregular motions of the fall are explained in terms of low-dimensional chaos.
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Tanabe et al. (1994) studied this question.