Multiplikatif Lorentz Geometride 1-Parametreli Hareketlerin Geometrik Bir Yaklaşımı

Abstract

Multiplikatif Lorentz düzleminin trigonometrik yapıları önceki çalışmalarda incelenmiş, multiplikatif Lorentz düzlem üzerindeki dönme ve hareket kavramları tanımlanmıştır. Bu çalışmada, multiplikatif Lorentz düzleminde tanımlı bir parametreli hareketler ele alınmaktadır. Multiplikatif kalkülüs yöntemleri kullanılarak hareketlerin temel özellikleri incelenmiş; hız bileşenleri, hız yasası ve hızlar arasındaki ilişkiler elde edilmiştir. Ayrıca, harekete ait hız bileşenleri, hız yasası ve hızlar arasındaki ilişkiler elde edilmiştir Buna ek olarak hareketin ivmeleri ve bunlar arasındaki bağıntılar türetilmiştir. Hareketlerin geometrik tanımlanmasında önemli olan hareketli koordinat sistemleri multiplikatif Lorentz ortamına uyarlanmıştır. Bu kapsamda, multiplikatif Lorentz hareketli çatısının diferansiyel denklemleri elde edilmiş ve karşılık gelen çarpımsal Pfaff biçimleri tanıtılmıştır. Ayrıca üçüncü bir multiplikatif Lorentz düzlemi tanımlanarak üç düzlem arasındaki bağıl hareketler incelenmiştir. Elde edilen sonuçlar, multiplikatif Lorentz kinematiğinin geliştirilmesine ve bu alandaki ileri çalışmalar için bir temel oluşturulmasına katkı sağlamaktadır.

Keywords

• Multiplikatif 1- parametreli Lorentz Hareketi
• Pol Noktaları
• Multiplikatif Lorentz İç Çarpımı
• Multiplikatif Hızlar
• Multiplikatif İvmeler

A Geometric Investigation of Multiplicative One-Parameter Motions in Lorentzian Geometry

Abstract

The trigonometric framework of the multiplicative Lorentzian plane, together with the notions of multiplicative rotations and motions, has been investigated in earlier studies. In this paper, parameterized motions defined on the multiplicative Lorentzian plane are examined. By employing multiplicative calculus, the fundamental properties of these motions are analyzed, and the velocity components, velocity law, and relationships among velocities are derived. Furthermore, acceleration quantities and their corresponding relations are obtained. To provide a geometric description of motion, moving coordinate systems are adapted to the multiplicative Lorentzian setting. In this context, the differential equations of the multiplicative Lorentzian moving frame are established, and the associated multiplicative Pfaffian forms are introduced. Moreover, a third multiplicative Lorentzian plane is defined, and the relative motions among the three planes are investigated. The results contribute to the development of multiplicative Lorentzian kinematics and provide a basis for future studies.

Keywords

• Multiplicative One- Parameter Lorentzian Motion
• Pole points
• Multiplicative Lorentz Inner Product
• Multiplicative Velocities
• Multiplicative accelerations

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