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

Blas Herrera; Jordi Pallares; Agustí Reventós

doi:10.1285/i15900932v36n2p37

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

Blas Herrera, Jordi Pallares, Agustí Reventós

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2016 Universitá del Salento. We provide a geometrical characterization of the instantaneous rotation centers O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).

Original language	English
Pages (from-to)	37-47
Journal	Note di Matematica
Volume	36
Issue number	2
DOIs	https://doi.org/10.1285/i15900932v36n2p37
Publication status	Published - 1 Jan 2016

Keywords

Geometry of flows
Structure of flows

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abstract = "{\textcopyright} 2016 Universit{\'a} del Salento. We provide a geometrical characterization of the instantaneous rotation centers O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).",

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author = "Blas Herrera and Jordi Pallares and Agust{\'i} Revent{\'o}s",

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AU - Pallares, Jordi

AU - Reventós, Agustí

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N2 - © 2016 Universitá del Salento. We provide a geometrical characterization of the instantaneous rotation centers O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).

AB - © 2016 Universitá del Salento. We provide a geometrical characterization of the instantaneous rotation centers O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).

KW - Geometry of flows

KW - Structure of flows

U2 - 10.1285/i15900932v36n2p37

DO - 10.1285/i15900932v36n2p37

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VL - 36

SP - 37

EP - 47

JO - Note di Matematica

JF - Note di Matematica

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