3-Boyutlu Galilean Uzayında Tüp Yüzeyler Üzerine Bir Araştırma

Year 2022, Volume: 25 Issue: 3, 1133 - 1142, 01.10.2022

Fatma Almaz , Mihriban Külahci

https://doi.org/10.2339/politeknik.747869

Cited By: 3

Abstract

Bu çalışmada, Galilean 3-uzayında tanımlanan eğri tarafından üretilen tüp yüzeyleri incelenmiş ve yüzeyler üzerindeki jeodeziklerin açıklanmasının bazı sonuçları da verilmiştir. Ayrıca, tüp yüzeyde jeodezik olma koşulları, spesifik enerjiyi oluşturmak için Clairaut's teoremi yardımıyla elde edildi. Spesifik enerjinin ve açısal momentumun fiziksel anlamı elbette ki fiziksel anlamın kendisiyle ilişkilidir. Sonuçlarımız tüp yüzeylerde elde edilen spesifik enerjinin ve açısal momentumun Galilean uzayında keyfi jeodezik eğri kullanılarak ifade edilebildiğini göstermektedir. Ayrıca, elde edilen ortalama ve Gauss eğrilikleri elde edilerek, bu yüzeyler için bazı karakterizasyonlar verildi.

Keywords

Galilean uzay, tüp yüzeyleri, jeodezik eğri, spesifik kinetik enerji, spesifik açısal momentum

A Survey on Tube Surfaces in Galilean 3-Space

Abstract

In this study, the tube surfaces generated by the curve defined in Galilean 3-space are examined and some certain results of describing the geodesics on the surfaces are also given. Furthermore, the conditions of being geodesic on the tubular surface are obtained with the help of Clairaut’s theorem, which allows us to constitute the specific energy. The physical meaning of the specific energy and the angular momentum is of course related with the physical meaning itself. Our results show that the specific energy and the angular momentum obtained on tubular surfaces can be expressed using arbitrary geodesic curve in Galilean space. In addition, some characterizations are given for these surfaces, with the obtained mean and Gaussian curvatures.

Keywords

Galilean space, tube surfaces, geodesic curve, specific kinetic energy, specific angular momentum

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