2099. The Euler-Savary Formula

Buckley, R.; Whitfield, Esther

doi:10.2307/3611330

Cited by 10 publications

(5 citation statements)

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“…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%

“…Also, in [4], the relation between velocities and accelerations is examined, and the Euler-Savary Equation (ESE) is calculated. ESE gives the relation between a point in the moving plane and the center of curvature of the trajectory drawn by this point in the fixed plane [6]. Using a similar approach, oneparameter planar motions are examined in the complex plane C (see in [4]) and ESE is obtained by presenting the relation between the curvatures of the trajectory curves (see in [1,23]).…”

Section: Introductionmentioning

confidence: 99%

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Hyperbolic Number Forms of the Euler-Savary Equation

ÇAĞLAR>

Gürses

2022

International Electronic Journal of Geometry

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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.

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“…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%

Section: Introductionmentioning

confidence: 99%

Hyperbolic Number Forms of the Euler-Savary Equation

ÇAĞLAR>

Gürses

2022

International Electronic Journal of Geometry

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“…Ikawa gave the relationship between the curvature of roulette and curvatures of these base curve and rolling curve, [31]. Euler-Savary formula is a well documented and an admitted formula in the literature and many scientists have contributed to the development of fundamental knowledge of Euler-Savary formula, [32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes

Gürses¹,

Yüce²

2019

deufmd

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In this present paper, we will take three affine Cayley-Klein planes into consideration: , A and . AA  and /  by evaluating their derivative formulae, velocity vectors and pole points. Also, we will observe moving coordinate system and after that, we will examine the canonical relative system for one-parameter planar motions in the affine CK-planes by using the notions of moving coordinate system. Moreover, Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, will be obtained with the help of canonical relative system for oneparameter motions in affine CK-planes planes by using the method given by H. R. Müller in 1956 [1].

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“…In the planar motion of two conjugate curves on one another, Euler-Savary formula gives the radius of curvature and center of path traced by a point, [1,2]. The complex number approach is an efficient technique which takes care of signs automatically rather than combined graphical and analytical methods.…”

Section: Introductionmentioning

confidence: 99%

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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2099. The Euler-Savary Formula

Cited by 10 publications

References 0 publications

Hyperbolic Number Forms of the Euler-Savary Equation

Hyperbolic Number Forms of the Euler-Savary Equation

On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes

Bobillier Formula for the Elliptical Harmonic Motion

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