Scopus
🔓 Açık Erişim YÖKSİS Eşleşti
Modeling of (n,m)-Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications
Fractal and Fractional · Aralık 2024
YÖKSİS Kayıtları
Modeling of (n,m)-Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications
Fractal and Fractional · 2024 SCI-Expanded
DOKTOR ÖĞRETİM ÜYESİ AZİZ YAZLA →
Modeling of (n,m)-Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications
Fractal and Fractional · 2024 SCI-Expanded
PROFESÖR MUHAMMED TALAT SARIAYDIN →
Makale Bilgileri
DergiFractal and Fractional
Yayın TarihiAralık 2024
Cilt / Sayfa8
Scopus ID2-s2.0-85213456427
Erişim🔓 Açık Erişim
Özet
In the present paper, regular spacelike spatial Minkowski Pythagorean hodograph (MPH) curves are characterized with rational rotation-minimizing frames (RRMFs). We define an Euler–Rodrigues frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (Formula presented.). Expressing the conditions provided by these curves in the form of a Minkowski–Hopf map that we define; it is aimed to establish a connection with the Lorentz force that occurs during the process of computer numerical control (CNC)-type sinker electronic discharge machines (EDMs). This approach is reinforced by split quaternion polynomials. We give conditions satisfied by MPH curves of low degree to be type (Formula presented.) and construct illustrative examples. In five-axis CNC machines, rotation-minimizing frames are used for tool path planning, and in this way, unnecessary rotations in the tool frame are prevented and tool orientation is provided. Since we obtain MPH curves with RRMF using the ERF, finally we define the Fermi–Walker derivative and parallelism along MPH curves with respect to the ERF and give applications.
Yazarlar (2)
1
Muhammed Talat Sariaydin
2
Aziz Yazla
Anahtar Kelimeler
Minkowski–Hopf map
Minkowski Pythagorean hodograph curve
rational rotation minimizing frame
split quaternion polynomial
type (n,m) curve
Kurumlar
Selçuk Üniversitesi
Selçuklu Turkey