Application of Inverted Pendulum in Laplace Transformation of Mathematics Physics

Authors

Trisonia Fitria , Wipsar Sunu Brams Dwandaru , Warsono , R. Yosi Aprian Sari , Dian Puspita Eka Putri , Adiella Zakky Juneid

DOI:

10.29303/jppipa.v9i7.2953

Published:

2023-07-25

Issue:

Vol. 9 No. 7 (2023): July

Keywords:

Inverted pendulum, Laplace transformation, Mathematics physics

Research Articles

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How to Cite

Fitria, T., Dwandaru, W. S. B. ., Warsono, Sari, R. Y. A. ., Putri, D. P. E. ., & Juneid, A. Z. . (2023). Application of Inverted Pendulum in Laplace Transformation of Mathematics Physics. Jurnal Penelitian Pendidikan IPA, 9(7), 5446–5452. https://doi.org/10.29303/jppipa.v9i7.2953

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Abstract

The Laplace transform is a technique used to convert differential equations into algebra, it is often used for the analysis of dynamic systems and inverted pendulum systems. An inverted pendulum is a mechanism that moves objects from one place to another and shows the function of its activity while walking. This system is widely used in various fields, for example in the fields of robotics, industry, technology and organics. In an inverted pendulum there is an inverted pendulum dynamic system with a reading and driving force. The type of research used is pure research with quantitative methods, the aim is to develop science that aims to find new theories and develop existing theories in natural science. The results of the study show that using the Laplace transform can make it easier to find solutions regarding the inverted pendulum system for a variety of conditions, both in the initial conditions and when given an additional force or load, so it is concluded the application of the Laplace transform is useful for understanding how an inverted pendulum system will react to various forces, loads and initial conditions, which can be used to predict how the system will operate in the real world.

References

Agarana, M. C., & Agboola, O. O. (2015). Dynamic analysis of damped driven pendulum using Laplace transform method. International Journal of Mathematics and Computation, 26(3), 98–109. Retrieved from https://core.ac.uk/download/pdf/32225869.pdf

Agarana, M. C., & Akinlabi, E. T. (2019). Lagrangian-Laplace dynamic mechanical analysis and modeling of inverted pendulum. Procedia Manufacturing, 35, 711–718. https://doi.org/10.1016/j.promfg.2019.06.013

Altland, A., & von Delft, J. (2019). Mathematics for Physicists. Cambridge University Press. https://doi.org/10.1017/9781108557917

Aranovskiy, S. V, Biryuk, A. E., Nikulchev, E. V, Ryadchikov, I. V, & Sokolov, D. V. (2019). Observer Design for an Inverted Pendulum with Biased Position Sensors. Journal of Computer and Systems Sciences International, 58(2), 297–304. https://doi.org/10.1134/S1064230719020023

Arfken, G. H. W. and F. H. (2013). Mathematical Methods for Physicist seventh Edition. Academic Press.

Arifin, A., Musthofa, M. W., & Sugiyanto, S. (2013). Aplikasi Transformasi Laplace Pada Rangkaian Listrik. Jurnal Fourier, 2(1), 45. https://doi.org/10.14421/fourier.2013.21.45-61

Arsyam, M., & Tahir, M. Y. (2021). Ragam jenis penelitian dan perspektif. Al-Ubudiyah: Jurnal Pendidikan Dan Studi Islam, 2(1), 37–47. https://doi.org/10.55623/au.v2i1.17

de Jesús Rubio, J. (2018). Discrete time control based in neural networks for pendulums. Applied Soft Computing, 68, 821–832. https://doi.org/10.1016/j.asoc.2017.04.056

Elzaki, T. M., Elzaki, S. M., & Hilal, E. M. A. (2012). Elzaki and Sumudu transforms for solving some differential equations. Global Journal of Pure and Applied Mathematics, 8(2), 167–173. Retrieved from https://www.kau.edu.sa/Files/856/Researches/62669_33699.pdf

Fahad, H. M., Rehman, M. ur, & Fernandez, A. (2023). On Laplace transforms with respect to functions and their applications to fractional differential equations. Mathematical Methods in the Applied Sciences, 46(7), 8304–8323. https://doi.org/10.1002/mma.7772

Firdaus, R. A., Rahmatulloh, M. A., Dzulkiflih, & Khoiro, M. (2023). Analisa Lagrange pada Dinamika Stroller Non-Holonomic Berbasis Komputasi Fisika. Jurnal Kolaboratif Sains, 6(7), 749–756. https://doi.org/10.56338/jks.v6i7.3831

Haider, J. A., Saeed, F., Lone, S. A., Almutlak, S. A., & Elkotb, M. A. (2023). Stochastically analysis by using fixed point approach of pendulum with rolling wheel via translational and rotational motion. Modern Physics Letters B, 2350183. https://doi.org/10.1142/S021798492350183X

Henner, V., Nepomnyashchy, A., Belozerova, T., & Khenner, M. (2023). Laplace Transform BT - Ordinary Differential Equations: Analytical Methods and Applications (V. Henner, A. Nepomnyashchy, T. Belozerova, & M. Khenner (eds.); pp. 239–252). Springer International Publishing. https://doi.org/10.1007/978-3-031-25130-6_7

Huang, X., Wen, F., & Wei, Z. (2018). Optimization of triple inverted pendulum control process based on motion vision. Eurasip Journal on Image and Video Processing, 2018(1). https://doi.org/10.1186/s13640-018-0294-6

Ji, W., Xiao, L., & Lin, Q. (2023). Experimental study of pure shear fracture in rock-type materials. Theoretical and Applied Fracture Mechanics, 125, 103899. https://doi.org/10.1016/j.tafmec.2023.103899

Khan, M. N., Haider, J. A., Wang, Z., Lone, S. A., Almutlak, S. A., & Elseesy, I. E. (2023). Application of Laplace-based variational iteration method to analyze generalized nonlinear oscillations in physical systems. Modern Physics Letters B, 2350169. https://doi.org/10.1142/S0217984923501695

Kishimoto, S., & Ohnuki, S. (2023). Computational Method for Specific Energy Loss by Fast Inverse Laplace Transform. IEEE Access, 11, 7117–7123. https://doi.org/10.1109/ACCESS.2023.3237853

Li, D., Yang, W., & Huang, R. (2023). The multidimensional differences and driving forces of ecological environment resilience in China. Environmental Impact Assessment Review, 98, 106954. https://doi.org/10.1016/j.eiar.2022.106954

Makkulau Makkulau, Susanti Linuwih, Purhadi Purhadi, & Muhammad Mashuri. (2010). Pendeteksian Outlier dan Penentuan Faktor-Faktor yang Mempengaruhi Produksi Gula dan Tetes Tebu dengan Metode Likelihood Displacement Statistic-Lagrange. Jurnal Teknik Industri, 12(2), 95–100. Retrieved from http://puslit2.petra.ac.id/ejournal/index.php/ind/article/view/18065

Malik, S., Hashemi, M. S., Kumar, S., Rezazadeh, H., Mahmoud, W., & Osman, M. S. (2022). Application of new Kudryashov method to various nonlinear partial differential equations. Optical and Quantum Electronics, 55(1), 8. https://doi.org/10.1007/s11082-022-04261-y

Moatimid, G. M., Amer, T. S., & Zekry, M. H. (2023). Analytical and numerical study of a vibrating magnetic inverted pendulum. Archive of Applied Mechanics, 93(6), 2533–2547. https://doi.org/10.1007/s00419-023-02395-3

Moss, L. S. (1992). Barbara H. Partee, Alice ter Meulen, and Robert E. Wall. Mathematical methods in linguistics. Studies in linguistics and philosophy, vol. 30. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1990, xx + 663 pp. In Journal of Symbolic Logic (Vol. 57, Issue 1). https://doi.org/10.2307/2275199

Nasution, B., Lulut Alfaris, & Siagian, R. C. (2023). Basic Mechanics of Lagrange and Hamilton as Reference for STEM Students. Jurnal Penelitian Pendidikan IPA, 9(2), 898–905. https://doi.org/10.29303/jppipa.v9i2.2920

Peker, H. A., Karaoǧlu, O., & Oturanç, G. (2011). The differential transformation method and pade approximant for a form of blasius equation. Mathematical and Computational Applications, 16(2), 507–513. https://doi.org/10.3390/mca16020507

Putra, J. H. S., & Agustinah, T. (2016). Kontrol Tracking Fuzzy Menggunakan Model Following untuk Sistem Pendulum Kereta. Jurnal Teknik ITS, 5(2). https://doi.org/10.12962/j23373539.v5i2.16300

Resti, N. C. (2017). Sifat-Sifat Sistem Pendulum Terbalik dengan Lintasan Berbentuk Lingkaran. Intensif, 1(1), 20. https://doi.org/10.29407/intensif.v1i1.537

Rizal, Y., & Mantala, R. (2016). Keseimbangan Sistem Pendulum Terbalik Beroda. Prosiding SNRT (Seminar Nasional Riset Terapan), 5662, 9–10. Retrieved from https://repository.poliban.ac.id/id/eprint/184/1/rizal2016keseimbangan.pdf

Susanto, E. (2023). Model dan Kendali Modular pada Pendulum Terbalik tipe Rotary. Jurnal Rekayasa Elektrika, 19(1). https://doi.org/10.17529/jre.v19i1.28262

Tin, P. T., Minh, T. H. Q., Trang, T. T., & Dung, N. Q. (2019). Using real interpolation method for adaptive identification of nonlinear inverted pendulum system. International Journal of Electrical and Computer Engineering (IJECE), 9(2), 1078. https://doi.org/10.11591/ijece.v9i2.pp1078-1089

Wijaya, A., Yulida, Y., & Faisal. (2015). Hubungan Antara Transformasi Laplace Dengan Transformasi Elzaki. 9(1), 12–19. https://doi.org/10.20527/epsilon.v9i1.4

Wilujeng, A. D., Ulfiyah, L., Annafiyah, A., & Taqiuddin, M. H. (2022). Pembuatan Material Komposit Berbahan Dasar Sabut Kelapa Dan Jerami Padi Sebagai Peredam Kebisingan. Jurnal Technopreneur (JTech), 10(1), 1–4. https://doi.org/10.30869/jtech.v10i1.889

Yudhi, Y. H. (2019). Transformasi Laplace Modifikasi Untuk Menyelesaikan Beberapa Persamaan Diferensial Biasa Linear. Bimaster : Buletin Ilmiah Matematika, Statistika Dan Terapannya, 8(1), 53–62. https://doi.org/10.26418/bbimst.v8i1.30522

Author Biographies

Trisonia Fitria, Universitas Negeri Yogyakarta

Wipsar Sunu Brams Dwandaru, Universitas Negeri Yogyakarta

Warsono, Universitas Negeri Yogyakarta

R. Yosi Aprian Sari, Universitas Negeri Yogyakarta

Dian Puspita Eka Putri, Universitas Negeri Yogyakarta

Adiella Zakky Juneid, Universitas Negeri Yogyakarta

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Copyright (c) 2023 Trisonia Fitria, Wipsar Sunu Brams Dwandaru, Warsono, R. Yosi Aprian Sari, Dian Puspita Eka Putri, Adiella Zakky Juneid

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