One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$ C J

Gürses, Nurten; Akbiyik, Mücahit; Yüce, Salîm

doi:10.1007/s00006-015-0598-x

Cited by 11 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which is the subset of the generalized complex plane C p was studied by Gürses et al [39]. Similar to that study, the oneparameter homothetic motions in the generalized complex plane C p have been given as follows briefly.…”

Section: Preliminariesmentioning

confidence: 92%

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

Eri̇şi̇r

2021

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this study, the planar kinematics has been studied in a generalized complex plane which is a geometric representation of the generalized complex number system. Firstly, the planar kinematic formulas with one parameter for homothetic motions in the generalized complex plane have been mentioned briefly. Then, the Steiner area formula given areas of the trajectories drawn by the points taken in a generalized complex plane have been obtained during the one-parameter planar homothetic motion. Finally, the Holditch theorem, which gives the relationship between these areas of trajectories, has been expressed for homothetic motions in a generalized complex plane. So, this theorem obtained in this study is the most general form of all Holditch theorems obtained so far.

show abstract

Section: Preliminariesmentioning

confidence: 92%

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

Eri̇şi̇r

2021

Advances in Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Here overlines are used to indicate that the particular quantity is directed. For detailed information, see the studies [1,4,6,17,22,23]…”

Section: Complex Number Forms Of the Esementioning

confidence: 99%

“…In analogy with complex motions, one-parameter motions in the hyperbolic plane H are defined by [38]. Also, ESE is determined by [13] in H. Additionally, considering generalized complex numbers (see in [20]), one-parameter planar motion and ESE are obtained in generalized complex number plane (see in [17]). In these studies, ESE is calculated based on the radius of the osculating circles and the diameter of the inflection circle.…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic Number Forms of the Euler-Savary Equation

ÇAĞLAR>

Gürses

2022

International Electronic Journal of Geometry

Self Cite

View full text Add to dashboard Cite

This study deals with hyperbolic number forms of Euler-Savary Equation (ESE) to find either the four special points on the pole ray. While obtaining the hyperbolic ESE forms, one-parameter planar motion is considered according to the osculating circles contacting at three infinitesimally close points. This approach with the hyperbolic number method gives more detailed information than the traditional method. As a final part, examples are given to show the utility of the practical way in the application.

show abstract

“…Moreover, by using Müller's method in complex plane Euler-Savary formula has been given in [7]. From this aspect the generalization of Euler-Savary formula in Euclidean, Lorentzian, and Galilean planes has been occurred in [5]. Also, in [8] Euler-Savary formula in the case of elliptical harmonic motion has obtained using the formalism of elliptic numbers.…”

Section: Introductionmentioning

confidence: 99%

Bobillier Formula for the Elliptical Harmonic Motion

Dündar

Ersoy

Pereira

2018

Analele Universitatii "Ovidius" Constanta - Seria Matematica

View full text Add to dashboard Cite

In this study, we have considered the elliptical harmonic motion which is the superposition of two simple harmonic motions in perpendicular directions with the same angular frequency and phase difference of π/2 . It is commonly recognized that a convenient formulation for problems in planar kinematics is obtained by using number systems. Here the elliptical numbers are used to derive the Bobillier formula with two different methods for aforesaid motion; the first method depends on the Euler-Savary formula and the second one uses the usual relations of the velocities and accelerations.

show abstract

One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$ C J

Cited by 11 publications

References 27 publications

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

Hyperbolic Number Forms of the Euler-Savary Equation

Bobillier Formula for the Elliptical Harmonic Motion

Contact Info

Product

Resources

About

One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$ C J

Cited by 11 publications

References 27 publications

A New Construction of Holditch Theorem for Homothetic Motions in C p

A New Construction of Holditch Theorem for Homothetic Motions in C p

Hyperbolic Number Forms of the Euler-Savary Equation

Bobillier Formula for the Elliptical Harmonic Motion

Contact Info

Product

Resources

About

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$

A New Construction of Holditch Theorem for Homothetic Motions in $C_{p}$