Starting Curve of Rolling Friction and Chaos.

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  • 転がり出し変位曲線とカオス
  • コロガリ ダシ ヘンイ キョクセン ト カオス

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Abstract

The starting curves of rolling friction have been used for study of bifurcation-chaotic characteristics. The curve has the parameters m, A and B, which can change the patterns of the curve. In the case of m=3, the curve is symmetric with respect to a vertical axis, and agrees fundamentally with the logistic equation. For 1<m<3, the peak value of the curve shifts to the left side. On the other hand, for m>3, the peak value shifts to the right side. In the case of m=4, the curve agrees with the equation proposed by Feigenbaum. Thus the equations (curves) shown here are expanded mathematical models which contain the map functions presented previously. The following properties were elucidated after studying simulated results of the bifurcation phenomenon. The vertical distance of bifurcation points decreases uniformly with increase of m. However, the threshold points of bifurcation occur most rapidly in the case of m=2, and move to larger values of A as m increases or decreases. Since parameter m is related to loss energy, it is suggested that the bifurcation phenomena are also closely related to the loss energy of a system.

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