3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras

Guo, Shuangjian; Wang, Shengxiang; Zhang, Xiao-Hui

doi:10.3390/math10142485

Cited by 1 publication

(1 citation statement)

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“…A general minimal parameterization of the kinematic equation of rigid body motion is presented, according to the authors' knowledge, for the first time in this paper. In further work, we will research what can be changed if we replace dual Lie algebra with dual mock Lie algebra [59,60] and how to define dual triple systems [61,62].…”

Section: Discussionmentioning

confidence: 99%

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

Condurache,

Popa

2023

Symmetry

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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.

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Section: Discussionmentioning

confidence: 99%