Publication detail

Special orthogonal matrices over dual numbers and their applications

HRDINA, J. VAŠÍK, P. MATOUŠEK, R.

Original Title

Special orthogonal matrices over dual numbers and their applications

English Title

Special orthogonal matrices over dual numbers and their applications

Type

journal article in Scopus

Language

en

Original Abstract

We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multi--axis machines error modeling. To study orthogonal and special orthogonal matrices over dual numbers $\mathbb D$ we show the explicit description for dimesnion two and three. In this way the multi--axis machines error modeling is set in the context of modern differential geometry and linear algebra.

English abstract

We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multi--axis machines error modeling. To study orthogonal and special orthogonal matrices over dual numbers $\mathbb D$ we show the explicit description for dimesnion two and three. In this way the multi--axis machines error modeling is set in the context of modern differential geometry and linear algebra.

Keywords

matrices; dual numbers; kinematics; error modeling; Weyl algebras

RIV year

2015

Released

19.06.2015

Pages from

121

Pages to

126

Pages count

6

Documents

BibTex


@article{BUT115147,
  author="Jaroslav {Hrdina} and Petr {Vašík} and Radomil {Matoušek}",
  title="Special orthogonal matrices over dual numbers and their applications",
  annote="We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multi--axis machines error modeling. To study orthogonal and special orthogonal matrices over dual numbers $\mathbb D$ we show the explicit description for dimesnion two and three. In this way the multi--axis machines error modeling is set in the context of modern differential geometry and linear algebra.",
  chapter="115147",
  howpublished="print",
  number="6",
  volume="2015",
  year="2015",
  month="june",
  pages="121--126",
  type="journal article in Scopus"
}