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- W1996918101 abstract "With the aim of representing physical rigid body motions, this article deals with the Euclidean displacement operators. Remaining as elementary as possible, an intrinsic mathematical formalism is presented with the use of affine geometry together with Lie's theory of groups. We start by defining a differential operator associated with the velocity field. Then, thanks to the Lie acceptance of the exponential function, we derive the formal Lie expression of finite displacements which are shown to be equivalent to affine direct orthonormal transformations. Lie sub-algebras of screw velocity fields lead to the description of the displacement sub-groups. The geometric modelling of small displacements is also evoked. This paper unifies elements previously published in [2] and [5]. On présente les principaux aspects de l'étude géométrique et cinématique du mouvement du corps rigide via la théorie mathématique des groupes de Lie. On montre en particulier que les torseurs forment une algébre de Lie et que les déplacements résultent de l'exponentiation des torseurs. La liste exhaustive des sous-groupes est obtenue par l'établissement des sous-algèbres de Lie de l'ensemble des torseurs. La modélisation des petits déplacements est aussi enrichie par la thérie de Lie." @default.
- W1996918101 created "2016-06-24" @default.
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- W1996918101 date "1994-01-01" @default.
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- W1996918101 title "The mathematical group structure of the set of displacements" @default.
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- W1996918101 doi "https://doi.org/10.1016/0094-114x(94)90021-3" @default.
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