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Journals / Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi / 2019 / Cilt: 21 - Sayı: 61

On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes

Afin Cayley-Klein Düzlemlerinde Hareketli Koordinat Sistemi ve Euler-Savary Formülü Üzerine

Salim YÜCE
Nurten GÜRSES
Pages
137–148
Publication Date
2022-10-15
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, will be obtained with the help of canonical relative system for oneparameter motions in affine CK-planes planes by using the method given by H.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this present paper, we will take three affine Cayley-Klein planes into consideration: , A P òò and  Pò .
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Key Findings & Data:The plane  Pò is a fixed plane relative to two other moving affine Cayley-Klein (CK)-planes.
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Conclusion & Impact:Moreover, Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, will be obtained with the help of canonical relative system for oneparameter motions in affine CK-planes planes by using the method given by H.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this present paper, we will take three affine Cayley-Klein planes into consideration: , A P òò and  Pò . The plane  Pò is a fixed plane relative to two other moving affine Cayley-Klein (CK)-planes. We will describe one-parameter motions / , / AA ò ò ò ò PP and /  òò PP and discuss the relationship between the motions / , / AA ò ò ò ò PP and /  òò PP by evaluating their derivative formulae, velocity vectors and pole points. Also, we will observe moving coordinate system and after that, we will examine the canonical relative system for one-parameter planar motions in the affine CK-planes by using the notions of moving coordinate system. Moreover, Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, will be obtained with the help of canonical relative system for oneparameter motions in affine CK-planes planes by using the method given by H. R. Müller in 1956 [1].

Özet

Bu çalışmada , A P òò ve  Pò üç afin Cayley-Klein düzlemi gözönüne alınmıştır.  Pò düzlemi diğer iki hareketli afin Cayley-Klein (CK)-düzlemine göre sabittir. Çalışmada bir parametreli / , / AA  ò ò ò ò PP ve /  òò PP hareketleri tarif edilecek; türev formülleri, hız vektörleri ve pol noktaları elde edilerek / , / AA  ò ò ò ò PP ve /  òò PP hareketleri arasındaki ilişki tartışılacaktır. Ayrıca afin (CK)-düzlemlerinde hareketli koordinat sistemi araştırılarak bu hareketli koordinat sisteminin kavramları ile kavramları bir parametreli hareketler için kanonik izafe sistemi incelenecektir. Bu ifadelere ek olarak, kanonik izafe sistemi yardımıyla afin (CK)-düzlemlerinde bir parametreli hareketler için yörünge eğrilerinin eğrilikleri arasındaki ilişkiyi veren Euler Savary formülü H. R. Müller tarafında 1956 yılında verilen metodla elde edilecektir [1].

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Cite This Article

YÜCE, S., GÜRSES, N. (2022). On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, Cilt: 21 - Sayı: 61, 137–148. https://ajindex.com/articles/491446

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