Sönümlemeli Sistemlerin Eşlenmesi Üzerine

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.

On Matched Pair of Dissipation Systems

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

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