Summary
Using discrete links, the axially rotating chain is mathematically modelled by nonlinear difference equations. The critical rotation rate is determined as a function of end weight and the number of links. Large nonlinear displacements are found numerically by shooting and bisection methods.
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Wang, C.Y. Stability and large displacements of a heavy rotating linked chain with an end mass. Acta Mechanica 107, 205–214 (1994). https://doi.org/10.1007/BF01201830
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DOI: https://doi.org/10.1007/BF01201830