PEMODELAN DINAMIKA TIPPE TOP (TT) DENGAN KENDALA NON-HOLONOMIK BERBASIS KOMPUTASI FISIKA PADA BIDANG DATAR (R^2×SO(3))
DOI:
https://doi.org/10.22437/jop.v7i1.14457Keywords:
Kendala non holonomik; Dinamika, Ruang Konfigurasi, Tippe Top (TT).Abstract
Pemodelan sistem dinamik dalam real time sangat penting dalam kemajuan teknologi otomatis yang berkembang pesat saat ini, seperti metode perencanaan sistem robotic. Artikel ini menjelaskan sistem dinamik benda tegar dengan kendala non-holonomic pada ruang konfigurasi . Metode yang digunakan adalah Motion Planning Network dan simulasi numeric dengan komputasi fisika yang dapat digunakan untuk sistem benda non-holonomik yang bergerak secara real-time dengan Pendekatan Jellet Invarian (JI). Pendekatan JI dapat menghasilkan persamaan sistem gerak dan mengevaluasi simulasi model benda dengan kendala non holonomik dan juga menampilkan hasil eksperimen dinamika benda tegar dalam ruang konfigurasi . Sistem gerak benda dengan kendala non holonomik yang digunakan adalah Tippe top (TT). TT adalah mainan yang mirip seperti gasing yang jika diputar dapat membalik sendiri dengan batangnya. Penulis berhasil mendeskripsikan dinamika gerak TT secara real time dengan syarat awal bervariasi pada ruang konfigurasi .
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References
Holm DD. Geometric Mechanics. 2011. DOI:10.1142/p802.
Ariska M, Akhsan H and Muslim M. Dynamic Analysis of Tippe Top on Cylinder’s Inner Surface with and Without Friction Based on Routh Reduction, in: J. Phys. Conf. Ser., 2020. DOI:10.1088/1742-6596/1467/1/012040.
Branicki M, Moffatt HK and Shimomura Y. Dynamics of an Axisymmetric Body Spinning on a Horizontal Surface. III. Geometry of Steady State Structures for Convex Bodies. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006; 462(2066): 371–390. DOI:10.1098/rspa.2005.1586.
Tembely, M.; Vadillo, D.; Soucemarianadin, A.; Dolatabadi, A. Numerical Simulations of Polymer Solution Droplet Impact on Surfaces of Different Wettabilities. Processes 2019, 7, 798, doi:10.3390/pr7110798.
Fokker AD. The Tracks of Tops’ Pegs on the Floor. Physica. 1952; 18(8–9): 497–502. DOI:10.1016/S0031-8914(52)80050-3.
Shimomura Y, Branicki M and Moffatt HK. Dynamics of an Axisymmetric Body Spinning on a Horizontal Surface. II. Self-Induced Jumping. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2005; 461(2058): 1753–1774. DOI:10.1098/rspa.2004.1429.
Rauch-Wojciechowski S, Sköldstam M and Glad T. Mathematical Analysis of the Tippe Top. Regular and Chaotic Dynamics. 2005; 10(4): 333–362. DOI:10.1070/RD2005v010n04ABEH000319.
Ueda T, Sasaki K and Watanabe S. Motion of the Tippe Top: Gyroscopic Balance Condition and Stability. SIAM Journal on Applied Dynamical Systems. 2005; 4(4): 1159–1194. DOI:10.1137/040615985.
Moffatt HK and Tokieda T. Celt Reversals: A Prototype of Chiral Dynamics. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2008; 138(2): 361–368. DOI:10.1017/S0308210506000679.
C. R ̈osmann, F. Hoffmann, and T. Bertram, “Kinodynamic trajectoryoptimization and control for car-like robots,†in2017 IEEE/RSJInternational Conference on Intelligent Robots and Systems (IROS).IEEE, 2017, pp. 5681–5686.
Kilin AA and Pivovarova EN. The Influence of the Rolling Resistance Model on Tippe Top Inversion. 2020; (February). Available from: http://arxiv.org/abs/2002.06335.
Bou-Rabee NM, Marsden JE and Romero LA. Tippe Top Inversion as a Dissipation-Induced Instability. SIAM Journal on Applied Dynamical Systems. 2004; 3(3): 352–377. DOI:10.1137/030601351.
Lewis AD. The Physical Foundations of Geometric Mechanics. Journal of Geometric Mechanics. 2017; 9(4): 411–437. DOI:10.3934/jgm.2017019.
Glad ST, Petersson D and Rauch-Wojciechowski S. Phase Space of Rolling Solutions of the Tippe Top. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2007; 3. DOI:10.3842/SIGMA.2007.041.
Ariska M, Akhsan H and Muslim M. Potential Energy of Mechanical System Dynamics with Nonholonomic Constraints on the Cylinder Configuration Space, in: J. Phys. Conf. Ser., 2020. DOI:10.1088/1742-6596/1480/1/012075.
A. H. Qureshi, A. Simeonov, M. J. Bency, and M. C. Yip, “Motionplanning networks,†in2019 International Conference on Robotics andAutomation (ICRA). IEEE, 2019, pp. 2118–2124.
Ariska M, Akhsan H and Zulherman Z. Utilization of Maple-Based Physics Computation in Determining the Dynamics of Tippe Top. Jurnal Penelitian Fisika dan Aplikasinya (JPFA). 2018; 8(2): 123. DOI:10.26740/jpfa.v8n2.p123-131.
Sriyanti I, Ariska M, Cahyati N and Jauhari J. Moment of Inertia Analysis of Rigid Bodies Using a Smartphone Magnetometer. Physics Education. 2020; 55(1). DOI:10.1088/1361-6552/ab58ba.
Ariska M, Akhsan H and Muslim M. Utilization of Physics Computation Based on Maple in Determining the Dynamics of Tippe Top, in: J. Phys. Conf. Ser., 2019. DOI:10.1088/1742-6596/1166/1/012009.
Ciocci MC and Langerock B. Dynamics of the Tippe Top via Routhian Reduction. Regular and Chaotic Dynamics. 2007; 12(6): 602–614. DOI:10.1134/S1560354707060032.
Ciocci MC, Malengier B, Langerock B and Grimonprez B. Towards a Prototype of a Spherical Tippe Top. Journal of Applied Mathematics. 2012; 2012. DOI:10.1155/2012/268537.
Zobova AA. Comments on the Paper by M.C. Ciocci, B. Malengier, B. Langerock, and B. Grimonprez “Towards a Prototype of a Spherical Tippe Top.†Regular and Chaotic Dynamics. 2012; 17(3–4): 367–369. DOI:10.1134/S1560354712030112.
Johnson JJ, et al. Dynamically Constrained Motion Planning Networks for Non-Holonomic Robots. 2020; . Available from: http://arxiv.org/abs/2008.05112.
Zobova AA. Analitical and Numerical Investigation of the Double-Spherical Tippe-Top Dynamics. n.d.; : 1–25.
Analysis G. Global Analysis of Dynamical Systems. Global Analysis of Dynamical Systems. 2001; . DOI:10.1887/0750308036.
Soodak H. A Geometric Theory of Rapidly Spinning Tops, Tippe Tops, and Footballs. American Journal of Physics. 2002; 70(8): 815–828. DOI:10.1119/1.1479741.
B. J. Cohen, S. Chitta, and M. Likhachev, “Search-based planningfor manipulation with motion primitives,†in Robotics and Automation (ICRA), 2010 IEEE International Conference on. IEEE, 2010, pp. 2902–2908.
Bou-Rabee NM, Marsden JE and Romero LA. Dissipation-Induced Heteroclinic Orbits in Tippe Tops. SIAM Review. 2008; 50(2): 325–344. DOI:10.1137/080716177.
Gray CG and Nickel BG. Constants of the Motion for Nonslipping Tippe Tops and Other Tops with Round Pegs. American Journal of Physics. 2000; 68(9): 821–828. DOI:10.1119/1.1302299.
Blankenstein G. Symmetries and Locomotion of a 2D Mechanical Network : The Snakeboard. 2003; (July): 1–16.
E. Huang, M. Mukadam, Z. Liu, and B. Boots, “Motion planning withgraph-based trajectories and gaussian process inference,†inRoboticsand Automation (ICRA), 2017 IEEE International Conference on, 2017,pp. 5591–5598.
Domercq C, et al. Hall B. 2015; : 7–8.
Raman, K.A.; Jaiman, R.K.; Lee, T.-S.; Low, H.-T. Dynamics of simultaneously impinging drops on a dry surface: Role of impact velocity and air inertia. J. Colloid Interface Sci.2017, 486, 265–276, doi:10.1016/j.jcis.2016.09.062.
Montgomery R. Geometric Mechanics. 2006; 209–220. DOI:10.1090/surv/091/15.
A. Faust, K. Oslund, O. Ramirez, A. Francis, L. Tapia, M. Fiser,and J. Davidson, “Prm-rl: Long-range robotic navigation tasks bycombining reinforcement learning and sampling-based planning,†in 2018 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2018, pp. 5113–5120..
Langerock B, Cantrijn F and Vankerschaver J. Routhian Reduction for Quasi-Invariant Lagrangians. Journal of Mathematical Physics. 2010; 51(2). DOI:10.1063/1.3277181.
Branicki M and Shimomura Y. Dynamics of an Axisymmetric Body Spinning on a Horizontal Surface. IV. Stability of Steady Spin States and the “rising Egg†Phenomenon for Convex Axisymmetric Bodies. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006; 462(2075): 3253–3275. DOI:10.1098/rspa.2006.1727.