Geometric characterization of the rotation centers of a particle in a flow


We provide a geometrical characterization of the instantaneous rotation centers \overrightarrow{O}\left(  p,t\right)  of a particle in a flow \mathcal{F} over time t. Specifically, we will prove that: a) at a specific instant t, the point \overrightarrow{O}\left(  p,t\right)  is the center of curvature at the vertex of the parabola which best fits the path-particle line \gamma\left(  t\right)  on its Darboux plane at p, and b) over time t, the geometrical locus of \overrightarrow{O}\left(p,t\right)  is the line of striction of the principal normal surface generated by \gamma\left(  t\right)  .

DOI Code: 10.1285/i15900932v36n2p37

Keywords: Geometry of flows; structure of flows

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