Bobillier Formula for the Elliptical Harmonic Motion-Reference-Cited by-同舟云学术

Bobillier Formula for the Elliptical Harmonic Motion

Published:2018-03-01 Issue:1 Volume:26 Page:103-110
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Dundar Furkan Semih¹,Ersoy Soley²,Pereira Nuno T. Sá³

Affiliation:

1. Department of Physics, Bogazici University, 34342 Bebek, Istanbul , Turkey

2. Department of Mathematics, Sakarya University, Serdivan, Sakarya , Turkey

3. CTO at iJET International Lisabona , Portugal

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2018-0006

Reference11 articles.

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3. [3] Ersoy, S. and Bayrak, N., Bobillier Formula for One Parameter Motions in the Complex Plane, J. Mechanisms Robotics, 4(2), 24501[4 pages], 2012.10.1115/1.4006195

4. [4] Fayet M., Bobillier Formula as a Fundamental Law in Planar Motion, ZAMM Z. Angew. Math. Mech., 82(3), 207-210, 2002.10.1002/1521-4001(200203)82:3<207::AID-ZAMM207>3.0.CO;2-T

5. [5] Gürses, N., Akbiyik, M. and Yüce, S., One-Parameter Homothetic Mo- tions and Euler-Savary Formula in Generalized Complex Number Plane CJ , Adv. Appl. Cli_ord Algebras 26 (2016), 115-136.10.1007/s00006-015-0598-x

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