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    Polar Decomposition of Unit Dual Quaternions

    Source: Journal of Mechanisms and Robotics:;2013:;volume( 005 ):;issue: 003::page 31001
    Author:
    Purwar, Anurag
    ,
    Ge, Q. J.
    DOI: 10.1115/1.4024236
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This paper seeks to extend the notion of polar decomposition (PD) from matrix algebra to dualquaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the PD of spatial displacements in Euclidean threespace that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigidbody displacements. It is shown in this paper that a dual quaternion representing an element of SE(3) can be decomposed into a pair of unit quaternions, called double quaternion, that represents an element of SO(4). Furthermore, this decomposition process may be interpreted as the projection of a point in fourdimensional space onto a unit hypersphere. An example is provided to illustrate that the results obtained from this dualquaternion based polar decomposition are same as those obtained from the matrix based polar decomposition.
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      Polar Decomposition of Unit Dual Quaternions

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    contributor authorPurwar, Anurag
    contributor authorGe, Q. J.
    date accessioned2017-05-09T01:01:13Z
    date available2017-05-09T01:01:13Z
    date issued2013
    identifier issn1942-4302
    identifier otherjmr_005_03_031001.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/152621
    description abstractThis paper seeks to extend the notion of polar decomposition (PD) from matrix algebra to dualquaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the PD of spatial displacements in Euclidean threespace that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigidbody displacements. It is shown in this paper that a dual quaternion representing an element of SE(3) can be decomposed into a pair of unit quaternions, called double quaternion, that represents an element of SO(4). Furthermore, this decomposition process may be interpreted as the projection of a point in fourdimensional space onto a unit hypersphere. An example is provided to illustrate that the results obtained from this dualquaternion based polar decomposition are same as those obtained from the matrix based polar decomposition.
    publisherThe American Society of Mechanical Engineers (ASME)
    titlePolar Decomposition of Unit Dual Quaternions
    typeJournal Paper
    journal volume5
    journal issue3
    journal titleJournal of Mechanisms and Robotics
    identifier doi10.1115/1.4024236
    journal fristpage31001
    journal lastpage31001
    identifier eissn1942-4310
    treeJournal of Mechanisms and Robotics:;2013:;volume( 005 ):;issue: 003
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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