Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

Keçilioğlu, Osman; Gündoğan, Halit

doi:10.1007/s00006-011-0318-0

Cited by 12 publications

(5 citation statements)

References 6 publications

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“…where c i , {i = 0, 1, 2, 3} , are the Lorentzian Euler parameters and g i , {i = 0, 1, 2, 3} , are as defined in equation (3).…”

Section: Mappings Of Spatial Kinematics In Lorentzian Spacementioning

confidence: 99%

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A Study On Geometry of Spatial Kinematics in Lorentzian Space

Turhan¹,

Ayyıldız²

2017

SDÜ Fen Bil Enst Der

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In this paper, we study geometry of mappings of spatial kinematics in Lorentzian space with the aid of dual number and split quaternion. Also, we give orthogonal rotation matrix A with respect to the Lorentzian Rodrigues parameters and the Lorentzian Euler parameters in such a space. Then, Study's soma is developed and used to define the mapping of spatial kinematics into points of a dual Lorentzian projective space. Lorentz Uzayında Uzaysal Kinematiklerin Geometrisi Üzerine Bir ÇalışmaAnahtar Kelimeler Dual sayı, Euler parametreleri, Lorentz uzay, Uzaysal kinematik, Split kuaterniyon Özet: Bu çalışmada, dual sayı ve split kuaterniyon yardımıyla Lorentz uzayında uzaysal kinematiklerin dönüşümlerinin geometrisi ele alınmıştır. Ayrıca, bu uzayda bir A ortogonal dönüşüm matrisi, Lorentziyen Rodrigues ve Euler parametrelerine göre verilmiştir. Son olarak, Study'nin "soma" olarak isimlendirdigi dönüşüm uzayı geliştirilmiş ve bu yapı bir dual Lorentz projektif uzayın noktaları içinde uzaysal kinematiklerin dönüşümünü tanımlamak için kullanılmıştır.

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“…where c i , {i = 0, 1, 2, 3} , are the Lorentzian Euler parameters and g i , {i = 0, 1, 2, 3} , are as defined in equation (3).…”

Section: Mappings Of Spatial Kinematics In Lorentzian Spacementioning

confidence: 99%

“…Obtained eight homogeneous coordinates divide into two sets of four, each of them represents a vector in a Euclidean 4−space. There are many papers in shed light on this elegant notion [3,5,6,11,12]. Especially, spatial kinematics of points and lines in Euclidean space have been studied by Ravani and Roth [9].…”

Section: Introduction and Notationsmentioning

confidence: 99%

A Study On Geometry of Spatial Kinematics in Lorentzian Space

Turhan¹,

Ayyıldız²

2017

SDÜ Fen Bil Enst Der

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“…On the other hand, the rotations in Minkowski space time are studied in (ġimĢek and Özdemir, 2016;Erdoğdu and Özdemir, 2015). In a different way, Lorentzian rotations are investigated with Lorentzian matrix multiplications in (Özdemir, 2016;Keçelioğlu et al, 2012). Then, homothetic Cayley formula and transformation are defined Rodrigues and Euler parameters for homothetic motion are obtained in (Gonzalez et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Kuaterniyon Bakış Açısı ile Doğru ve Hiperdüzlem Boyunca Yansımalar

Erdoğdu

2019

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, the reflections in and are investigated by unit quaternions. Firstly, a linear transformation is defined to describe reflections in with respect to the plane passing through the origin and orthogonal to the quaternion. Then some examples are given to discuss obtained results. Similarly, two linear transformations are stated which correspond to the reflection in with respect to the hyperplane passing through the origin and a reflection with respect to the line in the direction of the quaternion. Finally, the matrix representaions of these reflections are found and the eigenvalues, eigenvectors of them are given to analyse the geometric meaning in terms of the components of the quaternion for each case.

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“…The frame F is fixed, but the position of the moving frame M varies with the parameter t . A mechanism is occurred by constraining rigid bodies together with joints that connect their relative movements . For instance, mechanical hands, walking machines, and cooperating manipulators are mechanical systems that join these distinctions .…”

Section: Introductionmentioning

confidence: 99%

“…The motion of a rigid body is represented as a continuous sequence of displacements D(t) ∶ F → M. The frame F is fixed, but the position of the moving frame M varies with the parameter t. A mechanism is occurred by constraining rigid bodies together with joints that connect their relative movements. 9 For instance, mechanical hands, walking machines, and cooperating manipulators are mechanical systems that join these distinctions. 5 On the other hand, a planar mechanism is a structure that orbits of points in all parts of the structure lie on planes that are parallel to a ground plane.…”

Section: Introductionmentioning

confidence: 99%

Structure equations and constraint manifolds on Lorentz plane

Durmaz

Aktaş

Gündoğan

2018

Math Methods in App Sciences

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Calculating the structure equation of a chain is important to represent the position of the end link on the chain. Furthermore, the structure equation helps to determine the constraint manifold of the chain. The constraint manifold satisfies to make geometric interpretations about the form that is obtained. What is more, the constraint forced on the positions of the end link by the rest of the chain is represented by the manifold. In Lorentz space, the structure equations change according to the causal characters of the first link. In this paper, we attain the structure equations of a planar open chain in terms of the causal character of the first link in this space. Later, the constraint manifolds of the chain by using these equations are given. Some geometric comments about these manifolds are explained.

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Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

Cited by 12 publications

References 6 publications

A Study On Geometry of Spatial Kinematics in Lorentzian Space

A Study On Geometry of Spatial Kinematics in Lorentzian Space

Kuaterniyon Bakış Açısı ile Doğru ve Hiperdüzlem Boyunca Yansımalar

Structure equations and constraint manifolds on Lorentz plane

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