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Dynamics of Human Head and Eye Rotations Under Donders' Constraint

The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law...

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Published in:IEEE transactions on automatic control 2012-10, Vol.57 (10), p.2478-2489
Main Authors: Ghosh, B. K., Wijayasinghe, I. B.
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description The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in Appendix I. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In Appendix II, a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name "half angle rule," has been derived.
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B.</creatorcontrib><title>Dynamics of Human Head and Eye Rotations Under Donders' Constraint</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. 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Psychology</subject><subject>geodesics</subject><subject>Geometry</subject><subject>half angle rule</subject><subject>Head</subject><subject>Head movement</subject><subject>Law</subject><subject>Listing's Law</subject><subject>Mathematical analysis</subject><subject>Mathematical model</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Measurement</subject><subject>Muscles</subject><subject>Pattern recognition. Digital image processing. 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B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-2ffe56693aa45625b1fa43429a9d15d3314c814a47368d1eb5c5a949048064053</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Biological and medical sciences</topic><topic>Biomechanics. Biorheology</topic><topic>Computer science; control theory; systems</topic><topic>Differential geometry</topic><topic>Donders' law</topic><topic>Dynamic tests</topic><topic>Dynamics</topic><topic>Equations</topic><topic>Euler Lagrange equation</topic><topic>Exact sciences and technology</topic><topic>Eye and associated structures. Visual pathways and centers. Vision</topic><topic>Eye movements</topic><topic>eye/head movement</topic><topic>Eyes &amp; eyesight</topic><topic>Fundamental and applied biological sciences. Psychology</topic><topic>geodesics</topic><topic>Geometry</topic><topic>half angle rule</topic><topic>Head</topic><topic>Head movement</topic><topic>Law</topic><topic>Listing's Law</topic><topic>Mathematical analysis</topic><topic>Mathematical model</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Measurement</topic><topic>Muscles</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>potential control</topic><topic>Quaternions</topic><topic>Riemannian Metric</topic><topic>Sciences and techniques of general use</topic><topic>Theorems</topic><topic>Tissues, organs and organisms biophysics</topic><topic>Trajectories</topic><topic>Vectors</topic><topic>Vertebrates: nervous system and sense organs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ghosh, B. K.</creatorcontrib><creatorcontrib>Wijayasinghe, I. 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K.</au><au>Wijayasinghe, I. B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamics of Human Head and Eye Rotations Under Donders' Constraint</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2012-10-01</date><risdate>2012</risdate><volume>57</volume><issue>10</issue><spage>2478</spage><epage>2489</epage><pages>2478-2489</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in Appendix I. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. 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subjects Applied sciences
Artificial intelligence
Biological and medical sciences
Biomechanics. Biorheology
Computer science
control theory
systems
Differential geometry
Donders' law
Dynamic tests
Dynamics
Equations
Euler Lagrange equation
Exact sciences and technology
Eye and associated structures. Visual pathways and centers. Vision
Eye movements
eye/head movement
Eyes & eyesight
Fundamental and applied biological sciences. Psychology
geodesics
Geometry
half angle rule
Head
Head movement
Law
Listing's Law
Mathematical analysis
Mathematical model
Mathematical models
Mathematics
Measurement
Muscles
Pattern recognition. Digital image processing. Computational geometry
potential control
Quaternions
Riemannian Metric
Sciences and techniques of general use
Theorems
Tissues, organs and organisms biophysics
Trajectories
Vectors
Vertebrates: nervous system and sense organs
title Dynamics of Human Head and Eye Rotations Under Donders' Constraint
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