Basic Mechanics of Lagrange and Hamilton as Reference for STEM Students

Authors

Budiman Nasution , Lulut Alfaris , Ruben Cornelius Siagian

DOI:

10.29303/jppipa.v9i2.2920

Published:

2023-02-28

Issue:

Vol. 9 No. 2 (2023): February

Keywords:

Classic mechanics, Hamilton mechanics, Lagrange mechanics, Physics education, STEM student

Research Articles

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How to Cite

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
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Abstract

This paper discusses the use of Lagrangian and Hamiltonian dynamics as alternative approaches for understanding the motion of objects in classical mechanics. These approaches, which are based on different mathematical techniques, can provide a deeper understanding of the principles of classical mechanics and the motion of objects, but may not be covered in high school physics curricula or undergraduate STEM courses. The review paper approach is used to combine information from a variety of sources, and the material is conceptualized to aid reader understanding. These advanced topics may be of interest to advanced high school students who are interested in exploring topics beyond the high school physics curriculum, and can be studied independently by those with a strong foundation in classical mechanics and familiarity with advanced mathematical concepts.

References

Baleanu, D., Sadat Sajjadi, S., Jajarmi, A., & Asad, J. H. (2019). New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator. The European Physical Journal Plus, 134, 1–10, https://doi.org/10.1140/epjp/i2019-12561-x

Brahier, D. J. (2020). Teaching secondary and middle school mathematics. Routledge.

Cain, E. J., Akcaoglu, M., Wright, K., Dobson, A., & Elkins, T. (2022). “I’ve Always Loved Scienceâ€: A Qualitative Exploration of Rural College Students’ STEM Interest Development and Maintenance. Journal for STEM Education Research, 1–19.

Castellani, L., & D’Adda, A. (2020). Covariant hamiltonian for gravity coupled to p-forms. Physical Review D, 101(2), 025015, https://doi.org/10.1103/PhysRevD.101.025015

Chen, R., & Tao, M. (2021). Data-driven prediction of general Hamiltonian dynamics via learning exactly-symplectic maps. 1717–1727, https://doi.org/10.48550/arXiv.2103.05632

Erfan, M., & Ratu, T. (2018). Analysis of student difficulties in understanding the concept of Newton’s law of motion. JIPF (Jurnal Ilmu Pendidikan Fisika), 3(1), 1–4, https://dx.doi.org/10.26737/jipf.v3i1.161

Fichtner, A., & Zunino, A. (2019). Hamiltonian nullspace shuttles. Geophysical Research Letters, 46(2), 644–651, https://doi.org/10.1029/2018GL080931

Galili, I., & Goren, E. (2022). Summary lecture as a delay organizer of cultural content knowledge: The case of classical mechanics. Science & Education, 1–50, https://doi.org/10.3390/educsci13010095

García-Garrido, V. J., Agaoglou, M., & Wiggins, S. (2020). Exploring isomerization dynamics on a potential energy surface with an index-2 saddle using lagrangian descriptors. Communications in Nonlinear Science and Numerical Simulation, 89, 105331, https://doi.org/10.1016/j.cnsns.2020.105331

Hamm, K. (2020). 6.3 Newton’s Second Law of Motion: Concept of a System. Biomechanics of Human Movement.

Harlow, D., & Wu, J. (2020). Covariant phase space with boundaries. Journal of High Energy Physics, 2020(10), 1–52, https://doi.org/10.1007/JHEP10(2020)146

He, W., Tang, X., Wang, T., & Liu, Z. (2022). Trajectory tracking control for a three-dimensional flexible wing. IEEE Transactions on Control Systems Technology, 30(5), 2243–2250, https://doi.org/10.1109/TCST.2021.3139087

Hjelmstad, K. D., & Hjelmstad, K. D. (2022). Foundations of Dynamics. Fundamentals of Structural Dynamics: Theory and Computation, 1–21.

Impelluso, T. J. (2018). The moving frame method in dynamics: Reforming a curriculum and assessment. International Journal of Mechanical Engineering Education, 46(2), 158–191, https://doi.org/10.1177/0306419017730633

Insinga, A., Andresen, B., & Salamon, P. (2016). Thermodynamical analysis of a quantum heat engine based on harmonic oscillators. Physical Review E, 94(1), 012119, https://doi.org/10.1103/PhysRevE.94.012119

Jiroušek, P., Shimada, K., Vikman, A., & Yamaguchi, M. (2022). New Dynamical Degrees of Freedom from Invertible Transformations. ArXiv Preprint ArXiv:2208.05951.

Katsikadelis, J. T. (2020). Dynamic analysis of structures. Academic press.

Kersting, M., & Steier, R. (2018). Understanding Curved Spacetime: The Role of the Rubber Sheet Analogy in Learning General Relativity. Science & Education, 27, 593–623, https://doi.org/10.1007/s11191-018-9997-4

Koczan, G. M. (2021). New definitions of 3D acceleration and inertial mass not violating F= MA in the Special Relativity. Results in Physics, 24, 104121, https://doi.org/10.1016/j.rinp.2021.104121

Lee, J. G., Brooks, A. M., Shelton, W. A., Bishop, K. J., & Bharti, B. (2019). Directed propulsion of spherical particles along three dimensional helical trajectories. Nature Communications, 10(1), 2575, https://doi.org/10.1038%2Fs41467-019-10579-1

Li, W., Bazant, M. Z., & Zhu, J. (2021). A physics-guided neural network framework for elastic plates: Comparison of governing equations-based and energy-based approaches. Computer Methods in Applied Mechanics and Engineering, 383, 113933.

Ma, H. (2003). The nature of time and space. Nature and Science, 1(1), 1–11.

MacKay, R. S., & Meiss, J. D. (2020). Hamiltonian Dynamical Systems: A reprint selection. CRC Press.

Mandal, A., Tiwari, Y., Panigrahi, P. K., & Pal, M. (2022). Physics aware analytics for accurate state prediction of dynamical systems. Chaos, Solitons & Fractals, 164, 112670, DOI: 10.1016/j.chaos.2022.112670

Mann, P. (2018). Lagrangian and Hamiltonian dynamics. Oxford University Press.

Mattheakis, M., Protopapas, P., Sondak, D., Di Giovanni, M., & Kaxiras, E. (2019). Physical symmetries embedded in neural networks. ArXiv Preprint ArXiv:1904.08991.

Misbah, M. (2022). Persamaan Differensial Matematika Fisika.

Mishra, H., Garofalo, G., Giordano, A. M., & Ott, C. (2020). On the dynamics of floating-base robots: Linking the recursive formulation to the Reduced Euler-Lagrange Equations. Preprint, 10.

Musyrifah, S. P. (2022). Realasional Key (Super Key, Candidat Key, Primary Key, Alternatif). Basis Data, 43.

Nisa, R. (2018). Pengaruh pola asuh orang tua dan interaksi sosial terhadap hasil belajar mata pelajaran matematika siswa kelas IV di Madrasah Ibtidaiyah se-Kecamatan Lowokwaru Kota Malang.

Norbury, J. W. (2000). Lagrangians and Hamiltonians for high school students. ArXiv Preprint Physics/0004029.

North, J. (2021). Formulations of classical mechanics. In The Routledge Companion to Philosophy of Physics (pp. 21–32). Routledge.

Sedov, L. I. (2018). Similarity and dimensional methods in mechanics. CRC press.

Shaw, A., Gatti, G., Gonçalves, P., Tang, B., & Brennan, M. (2021). Design and test of an adjustable quasi-zero stiffness device and its use to suspend masses on a multi-modal structure. Mechanical Systems and Signal Processing, 152, 107354.

Simoneau, A. (2019). An Overview of Computational Mathematical Physics: A Deep Dive on Gauge Theories.

Sisini, F., & Sisini, V. (2021). The Turing machine of a harmonic oscillator: From the code to the dynamic system. ArXiv Preprint ArXiv:2110.06119.

Smith, F. T. (1960). Generalized angular momentum in many-body collisions. Physical Review, 120(3), 1058, https://doi.org/10.1103/PhysRev.120.1058

Sugiyama, H., Escalona, J. L., & Shabana, A. A. (2003). Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dynamics, 31(2), 167–195, https://doi.org/10.1023/A:1022082826627

Sutton, G. V. (2018). Science for a polite society: Gender, culture, and the demonstration of Enlightenment. Routledge.

Tigist, M. (2019). Hamiltonian Dynamics of Constrained Rigid BodY.

Tokasi, S. (2022). Lagrangian equations of motion of classical many body systems on shape space obeying the modified newtonian theory. ArXiv Preprint ArXiv:2208.00229.

Toto, T. (2018). Aplikasi Kalkulus dalam Perkuliahan Fisika. 2(1), 26–33.

Usubamatov, R. (2020). Theory of Gyroscopic effects for rotating objects. The Open Access Journal of Science and Technology, 1–1.

Verlinde, E. (2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 2011(4), 1–27, https://doi.org/10.48550/arXiv.1001.0785

Wallace, D. (2021). Probability and irreversibility in modern statistical mechanics: Classical and quantum, ArXiv Preprint ArXiv:2104.11223.

Wang, Q. A. (2005). Maximum path information and the principle of least action for chaotic system. Chaos, Solitons & Fractals, 23(4), 1253–1258, https://doi.org/10.1016/j.chaos.2004.06.046

Wu, Z., Furbish, D., & Foufoulaâ€Georgiou, E. (2020). Generalization of hop distanceâ€time scaling and particle velocity distributions via a twoâ€regime formalism of bedload particle motions. Water Resources Research, 56(1), e2019WR025116

Zain, S. (2019). Lagrangian mechanics. In Techniques of Classical Mechanics: From Lagrangian to Newtonian mechanics. IOP Publishing.

Zak, S. H. (2003). Systems and control (Vol. 198). Oxford University Press New York.

Zukhrufurrohmah, Z., & Putri, O. R. U. (2019). Rekognisi dalam merepresentasikan simbol turunan parsial sebagai metonymy dan metaphor. JINoP (Jurnal Inovasi Pembelajaran), 5(2), 214–226, https://doi.org/10.22219/jinop.v5i2.9659

Author Biographies

Budiman Nasution, Departemen of Physics, Faculty of Mathematics and Natural Science, Universitas Negeri Medan

Departemen of Physics, Faculty of Mathematics and Natural Science, Universitas Negeri Medan

Lulut Alfaris, Department of marine technology, Pangandaran marine and fisheries Polytechnic

Department of marine technology, Pangandaran marine and fisheries Polytechnic

Ruben Cornelius Siagian, Universitas Negeri Medan

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Copyright (c) 2023 Ruben Cornelius Siagian, Lulut Alfaris, Budiman Nasution

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