Discrete Lagrangian Dynamics on Matched Pair Lie Groups

Abstract

The Lagrangian formulation of the discrete dynamics on matched pair Lie groups is studied. As a result, the discrete matched Lagrange equations that manage the joint behavior of two discrete systems in mutual interaction are obtained. In particular, the discrete equations on the tangent group of a Lie group are presented. The results are illustrated on a matched pair group constructed on two copies of the Heisenberg group, and thus obtained discrete Lagrange equations are written with matrix notation.

Keywords

• Discrete Lagrange equations
• matched pair of Lie groups

EŞLENMİŞ LİE GRUPLARI ÜZERİNDEKİ LAGRANGE FARK DENKLEMLERİ

Abstract

Sürekli olmayan dinamiğin Lagrange formülasyonu eşlenmiş Lie gruplar üzerinde çalışılmıştır. Sonuç olarak, karşılıklı etkileşim altındaki kesikli iki sistemin dinamiğini tarif eden eşlenmiş fark denklemleri elde edilmiştir. Özel olarak da, bir Lie grubunun teğet grubu üzerindeki fark denklemleri ifade edilmiştir. Elde edilen sonuçlar, Heisenberg grubunun iki kopyası üzerine bina edilen bir eşlenmiş Lie grubu özelinde çalışılmış, ve elde edilen Lagrange fark denklemleri matris formunda yazılmıştır.

Keywords

• (Lagrange) fark denklemleri
• eşlenmiş Lie grupları
• eşlenmiş fark denklemleri

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