One-Parameter Planar Motions in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$ C J

Gürses, Nurten; Yüce, Salîm

doi:10.1007/s00006-015-0530-4

Cited by 11 publications

(1 citation statement)

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“…This system involves in complex (p = −1), dual (p = 0) and hyperbolic (p = +1) number systems and also different planes for other values of p. Considering the studies given by Yaglom and Harkins, some studies were done in the generalized complex plane. Gürses and Yüce considered the one parameter planar motion in Affine-Cayley Klein planes and p-complex plane C J = x + Jy : [19,20]. Moreover, Erişir et.…”

Section: Introductionmentioning

confidence: 99%

Holditch-Type Theorem for Non-Linear Points in Generalized Complex Plane $\mathbb{C}_{p}$

Eri̇şi̇r

Güngör

2018

Universal Journal of Mathematics and Applications

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The generalized complex number system and generalized complex plane were studied by Yaglom [1, 2] and Harkin [3]. Moreover, Holditch-type theorem for linear points in C p were given by Erişir et al. [4]. The aim of this paper is to find the answers of the questions "How is the polar moments of inertia calculated for trajectories drawn by non-linear points in C p ?", "How is Holditch-type theorem expressed for these points in C p ?" and finally "Is this paper a new generalization of [4]?".

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Section: Introductionmentioning

confidence: 99%

Holditch-Type Theorem for Non-Linear Points in Generalized Complex Plane $\mathbb{C}_{p}$

Eri̇şi̇r

Güngör

2018

Universal Journal of Mathematics and Applications

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On geometric interpretations of split quaternions

Öztürk

Özdemir

2022

Math Methods in App Sciences

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Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).

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