Autorotation

Invited Comment

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake.
Original languageEnglish
Article number023005
JournalPhysica Scripta
Volume91
Issue number2
Number of pages9
ISSN0281-1847
DOIs
Publication statusPublished - 2016

Keywords

  • Closed space curves
  • Darboux vector
  • DNA
  • Dirac belt trick
  • Integration of generalised Frenet Serret equations
  • Ribbon
  • Signed 3D curvature

Cite this

@article{a6638c6f4541446ebae734ae9726f244,
title = "Autorotation: Invited Comment",
abstract = "A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake.",
keywords = "Closed space curves, Darboux vector, DNA, Dirac belt trick, Integration of generalised Frenet Serret equations, Ribbon, Signed 3D curvature",
author = "Jakob Bohr and Steen Markvorsen",
year = "2016",
doi = "10.1088/0031-8949/91/2/023005",
language = "English",
volume = "91",
journal = "Physica Scripta. Topical Issues",
issn = "0281-1847",
publisher = "IOP Publishing",
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}

Autorotation : Invited Comment. / Bohr, Jakob; Markvorsen, Steen.

In: Physica Scripta, Vol. 91, No. 2, 023005, 2016.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Autorotation

T2 - Invited Comment

AU - Bohr, Jakob

AU - Markvorsen, Steen

PY - 2016

Y1 - 2016

N2 - A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake.

AB - A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake.

KW - Closed space curves

KW - Darboux vector

KW - DNA

KW - Dirac belt trick

KW - Integration of generalised Frenet Serret equations

KW - Ribbon

KW - Signed 3D curvature

U2 - 10.1088/0031-8949/91/2/023005

DO - 10.1088/0031-8949/91/2/023005

M3 - Journal article

VL - 91

JO - Physica Scripta. Topical Issues

JF - Physica Scripta. Topical Issues

SN - 0281-1847

IS - 2

M1 - 023005

ER -