MULTİPLİKATİF ANALİZDE BİR EĞRİ VEYA YÜZEYİN BAŞKA BİR EĞRİ VEYA YÜZEY ÜZERİNDEN YUVARLANMASI HARAKETİ ÜZERİNE

Abstract

Bu çalışma, "Multiplikatif Analizde eğrinin veya yüzeyin başka bir eğri veya yüzey üzerinde yuvarlanması" kavramını yeniden ele alıyor ve keyfi n boyutlu Multiplikatif Öklid uzaylarında homotetik hareketler çerçevesinde daha geniş bir formülasyon geliştiriyor. Makalenin bulguları şu şekilde özetlenebilir: Hareketin davranışı, n’in çift ya da tek tam sayı olmasından bağımsız olarak aynı kalmaktadır. Herhangi bir n boyutu için, homotetik hareketler, ilişkili polar yörüngelerin karşılıklı kayma ve yuvarlanma etkileşimi sergilediği düzenli hareketler sınıfını temsil eder. Her t anında, tek bir anlık kutup noktası benzersiz olarak belirlenebilir. Elde edilen sonuçlar, aynı alanda daha önce yayımlanmış çalışmalarla ilişkilendirilerek tartışılmıştır. Son olarak, homotetik ölçekleme katsayısının sürekli olarak e1=e olduğu durumda afin yapının özel bir durum olarak ortaya çıktığı çıktığı gösterilmiştir.

Keywords

• Multiplikatif Analiz
• Bir Parametreli Multiplikatif Homotetik Hareketler
• Kutup Noktaları

ON THE MOTION OF A CURVE OR SURFACE ROLLING OVER ANOTHER CURVE OR SURFACE IN MULTIPLICATIVE CALCULUS

Abstract

This study revisits the notion of “On the motion of a curve or surface rolling over another curve or surface in multiplicative calculus and develops a broader formulation of it within the framework of homothetic motions in Multiplicative Euclidean spaces of arbitrary dimension n. The findings of the paper may be outlined as follows: The behavior of the motion remains the same regardless of whether n is an even or an odd integer;for any dimension n, homothetic motions represent a class of regular motions, where the associated polar trajectories exhibit a mutual sliding and rolling interaction; at each instant t, a single instantaneous pole point can be uniquely determined. The results obtained here are discussed in relation to previously published investigations in the same area. As a final remark, it is shown that the a¢ ne situation appears as a special case in which the homothetic scaling factor is constantly equal to e1 = e.

Keywords

• Multiplicative Calculus
• One Parameter Multiplicative Homothetic Motions
• Pole Points

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