Gülsüm YÜCA, Yusuf YAYLI

Homothetic Motions and Dual Transformations

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.

Anahtar Kelimeler:

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

Homothetic Motions and Dual Transformations

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.,

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