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Journals / Cumhuriyet Science Journal / 2018 / Cilt: 39 - Sayı: 33

The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space

Lorentziyen 3-Uzayda Spacelike Yüzeylerin Kontak Yuvarlanmasinin İleri Kinematiği

Mehmet AYDINALP
Hasan Hüseyin UĞURLU
Mustafa KAZAZ
Pages
882–899
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

The influence of the relative curvatures and torsion on spin-rolling kinematics is clearly presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate the forward kinematics of spin-rolling motion without sliding of one spacelike surface on another spacelike surface along the spacelike contact trajectory curves of the surfaces in Lorentzian 3-space.
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Key Findings & Data:A Darboux frame method is adopted to develop instantaneous kinematics of spin-rolling motion, which occurs in a nonholonomic system.
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Conclusion & Impact:The influence of the relative curvatures and torsion on spin-rolling kinematics is clearly presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we investigate the forward kinematics of spin-rolling motion without sliding of one spacelike surface on another spacelike surface along the spacelike contact trajectory curves of the surfaces in Lorentzian 3-space. A Darboux frame method is adopted to develop instantaneous kinematics of spin-rolling motion, which occurs in a nonholonomic system. Then new kinematic formulations of spin-rolling motion of spacelike moving surface with respect to contravariant vectors, rolling velocity, and geometric invariants are obtained. The translational velocity formulation of an arbitrary point and the equation of the angular velocity formulation on the spacelike moving surface are derived. The equation, which is represented with geometric invariants, can be easily applied to arbitrary spacelike parametric surface and spacelike contact trajectory curve and can be differentiated to any order. The influence of the relative curvatures and torsion on spin-rolling kinematics is clearly presented.

Özet

Bu makalede, 3-boyutlu Lorentziyen uzayda bir spacelike yüzeyin bir diğer spacelike yüzey üzerinde yüzeylerin kontak spacelike yörünge eğrileri boyunca kaymaksızın dönme-yuvarlanma hareketinin ileri kinematiğini inceledik. Holonomik olmayan bir sistemde ortaya çıkan dönme-yuvarlanma hareketinin anlık kinematiğini kurmak için bir Darboux çatı metodu kullanılmıştır. Ardından, kontravaryant vektörler, yuvarlanma hızı ve geometrik değişmezlere göre hareketli spacelike yüzeyin dönme-yuvarlanma hareketinin yeni kinematik formülasyonları elde edilmiştir. Keyfi bir noktanın öteleme hızı formülasyonu ve hareketli spacelike yüzey üzerindeki açısal hız formülasyonunun denklemi elde edilmiştir. Geometrik değişmezlerle ifade edilen denklem, her mertebeden türevlenebilirdir ve keyfi spacelike parametrik yüzeye ve spacelike kontak yörünge eğrisine kolayca uygulanabilir. Dönme-yuvarlanma kinematiğinin bağıl eğrilikleri ve burulmasının etkisi açık olarak gösterilmektedir.

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Cite This Article

AYDINALP, M., UĞURLU, H. H., KAZAZ, M. (2022). The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space. Cumhuriyet Science Journal, Cilt: 39 - Sayı: 33, 882–899. https://ajindex.com/articles/477993

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