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Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral

  • Cunbiao Lee (a1), Zhuang Su (a1), Hongjie Zhong (a1), Shiyi Chen (a1), Mingde Zhou (a1) and Jiezhi Wu (a1)...

Abstract

The free-fall motion of a thin disk with small dimensionless moments of inertia ( ${I}^{\ast } \lt 1{0}^{- 3} $ ) was investigated experimentally. The transition from two-dimensional zigzag motion to three-dimensional spiral motion occurs due to the growth of three-dimensional disturbances. Oscillations in the direction normal to the zigzag plane increase with the development of this instability. At the same time, the oscillation of the nutation angle decreases to zero and the angle remains constant. The effects of initial conditions (release angle) were investigated. Two kinds of transition modes, zigzag–spiral transition and zigzag–spiral–zigzag intermittence transition, were observed to be separated by a critical Reynolds number. In addition, the solution of the generalized Kirchhoff equations shows that the small ${I}^{\ast } $ is responsible for the growth of disturbances in the third dimension (perpendicular to the planar motion).

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Corresponding author

Email address for correspondence: cblee@mech.pku.edu.cn

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