Effective Solutions for Moving Objects in Acceleration Functions and Their Reflections Using Goen's Distance Formula
DOI:
https://doi.org/10.25170/cylinder.v10i2.5952Keywords:
Goen distance formula, Mean integral, Symetric acceleration functionAbstract
Goen's distance formula effectively calculates the distance from acceleration, which has a pattern as a symmetric function of time changes. In Goen's distance formula, where the acceleration function against time has a symmetric pattern, it can be solved simply by performing a total integral and multiplying it by half of the total time. Symmetric acceleration functions can be constructed by combining certain functions with their reflections. In this study, the method of proving Goen's distance formula is carried out mathematically using single and double-level average integrals of symmetric functions. The advantage of Goen's distance formula compared to the conventional distance formula is that in finding the distance traveled by an object moving with a symmetric acceleration function, it will be more effective because it is sufficient to perform an integral once compared to having to do two integrals as done in the conventional method.
References
Goenawan, Stephanus Ivan. 2020 Comparison Simulation Analysis Of The Gradual Summation Of A Function With Recognition Of Direct Extrapolation Via In Series, IJASST Univ. Sanata Dharma, Yogyakarta.
Goenawan, Stephanus Ivan. Maret 2003. Deret Bertingkat Berderajat Satu dalam Teori Keteraturan, Metris. Vol.4, No.1 Jakarta, Unika Atma Jaya, p.50-56.
Goenawan, Stephanus Ivan. 2023. Comparison Of Goen's Double Integral Method And Conventional Double Integral Method For A Symmetric Function, Seminar Nasional Matematika, Statistika dan Aplikasinya 2023.
Goenawan, Stephanus Ivan. 2021. Integral Ganda Goen. HKI.
Russell C. Hibbeler (2009). "Kinematics and kinetics of a particle". Engineering Mechanics: Dynamics (12th ed.). Prentice Hall. p. 298. ISBN 978-0-13-607791-6.
Ahmed A. Shabana (2003). "Reference kinematics". Dynamics of Multibody Systems (2nd ed.). Cambridge University Press. ISBN 978-0-521-54411-5.
P. P. Teodorescu (2007). "Kinematics". Mechanical Systems, Classical Models: Particle Mechanics. Springer. p. 287. ISBN 978-1-4020-5441-9..
Klein, P., Becker, S., Küchemann, S., & Kuhn, J. (2021). Test of understanding graphs in kinematics: Item objectives confirmed by clustering eye movement transitions. Physical Review Physics Education Research, 17(1), 13102. https://doi.org/10.1103/PhysRevPhysEducRes.17.013102.
J. M. McCarthy and G. S. Soh, 2010, Geometric Design of Linkages, Springer, New York.
Nuo, Q., Huang, Y., & Lu, Z. (2023). Bicycle trajectory control based on kinematic and dynamical models. Academic Journal of Mathematical Sciences, 4(1), 32–43. https://doi.org/10.25236/AJMS.2023.040106.
Phillips, Jack (2007). Freedom in Machinery, Volumes 1–2 (reprint ed.). Cambridge University Press. ISBN 978-0-521-67331-0.
Tsai, Lung-Wen (2001). Mechanism design:enumeration of kinematic structures according to function (illustrated ed.). CRC Press. p. 121. ISBN 978-0-8493-0901-4.
Moon, Francis C. (2007). The Machines of Leonardo Da Vinci and Franz Reuleaux, Kinematics of Machines from the Renaissance to the 20th Century. Springer. ISBN 978-1-4020-5598-0.
Amin, B. D., Sahib, E. P., Harianto, Y. I., Patandean, A. J., Herman, & Sujiono, E. H. (2020). The interpreting ability on science kinematics graphs of senior high school students in South Sulawesi, Indonesia. Jurnal Pendidikan IPA Indonesia, 9(2), 179–186. https://doi.org/10.15294/jpii.v9i2. 23349.
Downloads
Published
How to Cite
License
Copyright (c) 2024 Cylinder : Jurnal Ilmiah Teknik Mesin
This work is licensed under a Creative Commons Attribution 4.0 International License.
