Application of Inverted Pendulum in Laplace Transformation of Mathematics Physics
DOI:
10.29303/jppipa.v9i7.2953Published:
2023-07-25Downloads
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.
Keywords:
Inverted pendulum Laplace transformation Mathematics physicsReferences
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
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