PRESENTATION MULTIPLICATIVE COMPOSITIONS WITH FOUR VECTORS BY QUATERNIONIC MATRICES
DOI:
https://doi.org/10.15587/1729-4061.2010.3110Keywords:
quaternion matrices, vector matrices, multiplicative composition, the identity of vector algebraAbstract
It is proposed to use quaternionic matrices for presentation of vector algebra multiplicative compositions, that have scalar and outer products of four vectors. New formulas of matrix presentation of vector algebra operations are found. These formulas are directly adapted to computing experiment.References
- Акивис М.А. Тензорное исчисление. / М.А. Акивис, В.В. Гольдберг – М.: Наука, 1969. -352с.
- Борисенко А.И. Векторный анализ и начала тензорного исчисления. / А.И. Борисенко, И.Е. Тарапов – Харьков: «Вища школа», 1978. – 216с.
- Кильчевский Н.А. Курс теоретической механики / Н.А. Кильчевский. – М.: Наука, 1977. – т. 1. – 480с.; т. 2. – 544с.
- Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. – М.: Наука, 1984. – 832с.
- Кравець Т.В. Представлення кватерніонними матрицями послідовності скінчених поворотів твердого тіла у просторі. / Кравець Т.В. // Автоматика-2000. Міжнародна конференція з автоматичного управління: Праці у 7-ми томах. – т.2. – Львів: Державний НДІ Інформаційної інфраструктури, 2000. – с.140-145.
- Кравец Т.В. Об использовании кватернионных матриц для описания вращательного движения твердого тела в пространстве. / Т.В. Кравец // Техническая механика. – 2001. - №1. – с.148-157.
- Кравец В.В. Описание кинематики и нелинейной динамики ассиметричного твердого тела кватернионными матрицами. / В.В. Кравец, Т.В. Кравец, А.В. Харченко // Прикладная механика. – 2009. – Том 45. – №2 – с.133- 143.
- Кравец В.В. Мультипликативные композиции матриц, эквивалентных не равным и противоположным векторам. / В.В. Кравец, Т.В. Кравец, А.В. Харченко // Восточно-Европейский журнал передовых технологий. – 2010. – 2/9 (44) – с.56-61.
- Кравец В.В. Метод матричного представления мультипликативных композиций векторной алгебры. / В.В. Кравец, Т.В. Кравец, А.В. Харченко // Восточно-Европейский журнал передовых технологий. – 2010. – 3/6 (45) – с.12-17.
- Kravets V.V. Evaluation of the Centrifugal, Coriolis, and Gyroscopic Forces on a Railroad Vehicle Moving at High Speed / V.V. Kravets, T.V. Kravets // Int. Appl. Mech. – 2008. – 44. №1. – p. 101-109.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Виктор Владимирович Кравец, Александр Валерьевич Харченко, Тамила Викторовна Кравец
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
