Homothetic Motions and Dual Transformations

Year 2021, Volume: 37 Issue: 1, 194 - 205, 28.04.2021

Gülsüm Yüca , Yusuf Yaylı

Abstract

In this research, we produce a homothetic motion in E_1^n from a homothetic motion in E^n by using a dual transformation. Furthermore, we define a transition from Euclidean umbrella matrix to Lorentzian umbrella matrix. Then, we examine the invariance of the axis of the umbrella motion that is x ⃗=(1,1,..,1) in both spaces. We also provide examples to make our results clear. Moreover, we draw their figures to investigate visual representations. Finally, we study on homothetic motions in dual spaces.

Keywords

Homothetic Motion, Umbrella Motion, Dual Transformation, Lorentzian Space, Dual Space, Kinematics.

Homothetic Motions and Dual Transformations

Abstract

Bu çalışmada, dual dönüşüm yardımıyla E_1^n deki homotetik hareketlerden E^n de homotetik hareketler elde ettik. Ayrıca, Öklidyen şemsiye matrisleri ile Lorentzian şemsiye matrisleri arasında bir geçiş sağladık. Daha sonra, şemsiye hareketinin ekseni olan x ⃗=(1,1,..,1) in iki uzayda da sabit kaldığını gösterdik. Elde edilen sonuçların pekiştirilmesi amacıyla örnekler vererek şekillerini çizdik. Son olarak, homotetik hareketleri dual uzaylarda çalıştık.

Keywords

Homotetik Hareket, Şemsiye Hareketi, Dual Dönüşüm, Lorentz Uzayı, Dual Uzay, Kinematik

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