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A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions.
- Source :
-
Symmetry (20738994) . Nov2023, Vol. 15 Issue 11, p2011. 23p. - Publication Year :
- 2023
-
Abstract
- The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUATERNIONS
*PARAMETERIZATION
*LIE groups
*INITIAL value problems
*LIE algebras
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 15
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 173865303
- Full Text :
- https://doi.org/10.3390/sym15112011