Elliptical Harmonic Motion and Euler–Savary Formula

Pereira, Nuno T. Sá; Ersoy, Soley

doi:10.1007/s00006-015-0609-y

Cited by 9 publications

(7 citation statements)

References 11 publications

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“…22 There are some of studies on elliptic numbers in literature. [16][17][18][19][20][21][22][23][24][25] The elliptic biquaternion algebra is a four-dimensional vector space over C p . It is represented as…”

Section: Preliminariesmentioning

confidence: 99%

On the matrix algebra of elliptic biquaternions

Özen

Tosun

2019

Math Methods in App Sciences

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In this study, we introduce the concept of elliptic biquaternion matrices. Firstly, we obtain elliptic matrix representations of elliptic biquaternion matrices and establish a universal similarity factorization equality for elliptic biquaternion matrices. Afterwards, with the aid of these representations and this equality, we obtain various results on some basic topics such as generalized inverses, eigenvalues and eigenvectors, determinants, and similarity of elliptic biquaternion matrices. These valuable results may be useful for developing a perfect theory on matrix analysis over elliptic biquaternion algebra in the future.

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Section: Preliminariesmentioning

confidence: 99%

On the matrix algebra of elliptic biquaternions

Özen

Tosun

2019

Math Methods in App Sciences

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“…This is a study expanding aspects of [8] which deals with superposition of two simple harmonic motions in perpendicular directions with the same angular frequency and phase difference of π/2. If a point has two component simple harmonic motions in any directions with the same periods the resultant motion of the point will be harmonic in an ellipse.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [8] authors represented elliptical harmonic motions in terms of elliptic numbers and elliptical trigonometry.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [8] by considering these basic notions and handling the mobile elliptical planes A, E and fixed elliptical planes E with coordinate systems {B; a 1 , a 2 }, {O; e 1 , e 2 } and {O ; e 1 , e 2 }, respectively, the Euler-Savary formula for elliptical harmonic motions was given as follows.…”

Section: Preliminariesmentioning

confidence: 99%

“…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%

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Bobillier Formula for the Elliptical Harmonic Motion

Dündar

Ersoy

Pereira

2018

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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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.

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