Year 2017, Volume 21, Issue 3, Pages 469 - 480 2017-06-01

Dinamik Sistemlerin Eşlenmesi
Matching of Dynamical Systems

Oğul Esen [1]

353 691

Karşılıklı etki-tepki içindeki iki fiziksel sistemin ortak hareketlerini veren denklemler (eşlenmiş Lie-Poisson ve
eşlenmiş Euler-Poincaré) elde edilecektir. Eşlenmiş denklemlerin literatürde çokça çalışılmış yarı-direkt çarpım
teorisinin genişlemesi olduğu gösterilecektir. İki örnek verilecektir. İlki, köşegen elemanları 1 olan alt ve üst
üçgensel matris gruplarının oluşturduğu eşlenmiş Lie grubu üzerinde eşlenmiş Lie-Poisson denklemlerinin
yazılmasıdır. İkinci örnek ise ikinci sınıf nilpotent grupların kendiyle eşlenmesi ile elde edilecek Lie grupları
üzerinde eşlenmiş hareket denklemlerinin yazılmasıdır. İki yeni açık problem sunulacaktır. Bunlardan ilki, plazma ve
akışkan arasında pür geometrik yapının eşlenmiş dinamik düzleminde ele alınması, diğeri ise karşılıklı etki-tepki
içindeki iki kesikli sistemin eşlenmesidir.
  

The equations (matched Lie-Poisson and matched Euler-Poincaré) are written for a couple of mutually interacting
physical systems. It is shown that the matched dynamics is a generalization of the well-developed semi-direct
product theory. Two examples are provided. The first one is to write the matched equations for the matched pair of
upper and lower triangular matrix groups whose diagonal entries are 1. The second example is to write the matched
equations for the Lie group obtained by matching a nilpotent group of class two by itself. Two new open problems
are presented. One of these is to write pure geometric relation between the plasma and fluid in the framework of the
matched dynamics. The other is to match two discrete systems under mutual interaction.
  

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Subjects Mathematics
Published Date Haziran 2017
Journal Section Research Articles
Authors

Author: Oğul Esen

Bibtex @research article { saufenbilder298954, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya University}, year = {2017}, volume = {21}, pages = {469 - 480}, doi = {10.16984/saufenbilder.298954}, title = {Matching of Dynamical Systems}, key = {cite}, author = {Esen, Oğul} }
APA Esen, O . (2017). Matching of Dynamical Systems. Sakarya University Journal of Science, 21 (3), 469-480. DOI: 10.16984/saufenbilder.298954
MLA Esen, O . "Matching of Dynamical Systems". Sakarya University Journal of Science 21 (2017): 469-480 <http://www.saujs.sakarya.edu.tr/issue/26996/298954>
Chicago Esen, O . "Matching of Dynamical Systems". Sakarya University Journal of Science 21 (2017): 469-480
RIS TY - JOUR T1 - Matching of Dynamical Systems AU - Oğul Esen Y1 - 2017 PY - 2017 N1 - doi: 10.16984/saufenbilder.298954 DO - 10.16984/saufenbilder.298954 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 469 EP - 480 VL - 21 IS - 3 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.298954 UR - https://doi.org/10.16984/saufenbilder.298954 Y2 - 2017 ER -
EndNote %0 Sakarya University Journal of Science Matching of Dynamical Systems %A Oğul Esen %T Matching of Dynamical Systems %D 2017 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 21 %N 3 %R doi: 10.16984/saufenbilder.298954 %U 10.16984/saufenbilder.298954
ISNAD Esen, Oğul . "Matching of Dynamical Systems". Sakarya University Journal of Science 21 / 3 (June 2017): 469-480. https://doi.org/10.16984/saufenbilder.298954