Sönümlemeli Sistemlerin Eşlenmesi Üzerine

Year 2021, Volume: 21 Issue: 2, 273 - 282, 30.04.2021

Oğul Esen , Gökhan Özcan , Serkan Sütlü

https://doi.org/10.35414/akufemubid.803443

Abstract

Bu makalede karşılıklı etki tepki içindeki iki sönümlemeli sistemin beraber (kollektif- eşlenmiş) hareketinin analizi üzerine bir yöntem öneriyoruz. Aşikardır ki; eşlenmiş hareketi kontrol eden diferansiyel denklemler iki sistemin denklemlerini bir arada yazmak dışında karşılıklı etki tepkinin doğurduğu fazladan terimler içerecektir. Karşılıklı etkiyi belirleyen ilave terimler, Lie cebirlerinin karşılıklı etkisi ile üretilecektir ve bu şekilde pür geometrik/cebirsel bir inşa gerçekleştirilecektir. Sonrasında elde ettiğimiz sonuçları 3 ve 4 boyutlu örneklerde göstereceğiz.

Keywords

eşlenmiş Lie cebirleri, Metriplektik sistemler, Rayleigh sönümlemesi, Cartan–Killing metriği

Supporting Institution

tübitak

Project Number

117F426

Thanks

Bu çalışma TÜBİTAK’ın (Türkiye Bilimsel ve Teknolojik Araştırma Kurumu) 117F426 proje numarasıyla “Eşlenmiş Lagrange Ve Hamilton Sistemleri” başlıklı proje kapsamında yapılmıştır. Tüm yazarlar desteği için TÜBİTAK’a müteşekkirdir.

On Matched Pair of Dissipation Systems

Abstract

In this work we propose a method to analyse the collective motion of two mutually interacting dissipative systems. It is obvious that; the differential equations controlling the matched motion will include extra terms generated by the mutual interactions, apart from writing the equations of the two systems together. These additional terms will be produced in this work by the mutual actions of Lie algebras, and in this way a pure geometric / algebraic construction will be realized. We shall then illustrate our results on 3 and 4 dimensional examples.

Keywords

Matched Lie Algebras, Metriplectic Systems, Rayleigh Dİssipation, Cartan-Killing metric

Project Number

117F426

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