PLANE KINEMATICS IN HOMOTHETIC MULTIPLICATIVE CALCULUS

Year 2024, Volume: 7 Issue: 1, 37 - 47, 31.01.2024

Hasan Es

https://doi.org/10.33773/jum.1408506

Cited By: 1

Abstract

In this study, pole points of motion, pole trajectories, velocities, accelerations and relations
between velocities and accelerations are obtained. In addition we gave some new theorems

Keywords

One Parameter homothetic multiplicative motion;, Pole point;, Pole curve

References

• A. E. Bashirov, M. R\i za, On Complex multiplicative differentiation, TWMS J. App. Eng. Math. Vol.1, No.1, pp.75-85 (2011).
• A. E. Bashirov, E. Mısırlı , Y. Tandoğdu, A. Ozyapıcı , On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Vol.26, No.4, pp.425-438 (2011).
• A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008).
• K. Boruah and B. Hazarika, Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces, J. Math. Anal. Appl., Vol.449, No.2, pp.1265-1285 (2017).
• K. Boruah and B. Hazarika, Some basic properties of G-Calculus and its applications in numerical analysis, arXiv:1607.07749v1 (2016).
• A. F. Çakmak, F. Başar, On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. Art. ID 932734, 12 pages (2012).
• E. Misirli and Y. Gurefe, Multiplicative Adams Bashforth--Moulton methods, Numer. Algor. Vol.57, pp.425-439 (2011).
• A. F. Çakmak, F. Başar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. Vol.6, No.1, pp.27-37 (2015).
• D. Campbell, Multiplicative Calculus and Student Projects, Vol.9, No.4, pp.327-333 (1999).
• M. Coco, Multiplicative Calculus, Lynchburg College, (2009).
• M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts (1972).
• M. Grossman, Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts (1983).
• M. Grossman, An Introduction to non-Newtonian calculus, Int. J. Math. Educ. Sci. Technol. Vol.10, No.4, pp.525-528 (1979).
• J. Grossman, M. Grossman, R. Katz, The First Systems of Weighted Differential and Integral Calculus, University of Michigan (1981).
• J. Grossman, Meta-Calculus: Differential and Integral, University of Michigan (1981).
• Y. Gurefe, Multiplicative Differential Equations and Its Applications, Ph.D. in Department of Mathematics (2013).
• W.F. Samuelson, S.G. Mark, Managerial Economics, Seventh Edition (2012).
• D. Stanley, A multiplicative calculus, Primus IX 4, pp.310-326 (1979).
• S. Tekin, F. Başar, Certain Sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal. Article ID 739319, 11 pages (2013).
• C. Türkmen and F. Başar, Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1. Vol.61, No.2, pp.17-34 (2012).
• A. Uzer, Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. Vol.60, pp.2725-2737 (2010).
• K. Boruah and B. Hazarika, G-Calculus, TWMS J. App. Eng. Math. Vol.8, No.1, pp. 94-105 (2018).
• S. Aslan, M. Bekar, Y. Yaylı, Geometric 3-space and multiplicative quaternions, International Journal 1 of Geometric Methods in Modern Physics, Vol.20, No.9 (2023).
• S. Nurkan, K. İ. Gürgil, M. K. Karacan, Vector properties of geometric calculus, Math. Meth. Appl. Sci. pp.1-20 (2023).
• H. Es, On The 1-Parameter Motions With Multiplicative Calculus, Journal of Science and Arts, Vol.2, No.59, (2022).