APPLICATION OF JMODELICA.ORG TO TEACHING THE FUNDAMENTALS OF DYNAMICS OF FOUCAULT PENDULUM-LIKE GUIDED SYSTEMS TO ENGINEERING STUDENTS

Keywords: Foucault pendulum-like system, mechanical engineering education, JModelica.org & Optimica freeware, crane arm guided rotation, open-loop load swaying control problem, acausal programming

Abstract

The present educational research is focused on the solution of didactic problem of an engineering-friendly description and explanation of the dynamics and control of Foucault pendulum-like systems, which have arisen from practical problems of boom crane dynamics in lifting-and-handling machinery and transport. An educational actuality of the present research is grounded on the absence of a proper description and explanation of this topic in available textbooks and scientific articles in the fields of classical mechanics, control engineering, transport, lifting-and-handling machinery, engineering education, mechanical engineering education, and classical mechanics education. Among learning tools this article uses the following educational techniques: Modelica-assisted simulation with acausal equation-based freeware computer system JModelica.org with Optimica extension, physical simulation techniques, allegoric fairy tale analogy, didactic transposition method and a complex of individual Modelica-enhanced students’ computational assignments. The proposed educational approach provides a broadening of students’ ideas concerning the applicability of abstract physical concepts to the theory and practice of freeware-assisted mechanical engineering education of undergraduate and graduate students majoring in dynamics and control of guided lifting-and-handling machinery. Research finding, concepts and ideas of this research have found a practical educational application through the formulation of practical computational problems of term design works, planning of MSc degree students’ works, and freeware-enhanced curriculum of Donbass State Engineering Academy, Kramatorsk, Ukraine.

Author Biographies

Alexander V. Perig, Donbass State Engineering Academy, Kramatorsk
Ph.D. (Material Pressure Forming), Master (Physics Education), Associate Professor of Manufacturing Processes and Automation Engineering Department
Alexander A. Kostikov, Donbass State Engineering Academy, Kramatorsk
Ph.D. (Differential Equations), Master (Applied Mathematics), Associate Professor of Informatics and Engineering Graphics Department
Violetta M. Skyrtach, Donbass State Engineering Academy, Kramatorsk
Ph.D. (Ontology and Epistemology), Master (Philosophy Education), Associate Professor of Department of Philosophy, Socio-Political and Legal Sciences
Ruslan R. Lozun, Donbass State Engineering Academy, Kramatorsk
Master (Automation and Computer-Integrated Technologies), Ph.D. Applicant (Ph.D. Candidate) of Manufacturing Processes and Automation Engineering Department
Alexander N. Stadnik, Donbass State Engineering Academy, Kramatorsk
Master (Applied Mechanics), Senior Lecturer of the Department of Technical Mechanics

References

A. Z. Al-Garni, K. A. F. Moustafa, and S. S. A. K. Javeed Nizami, “Optimal control of overhead cranes”, Control Engineering Practice, vol. 3, no. 9, pp. 1277-1284, Sep. 1995. doi:10.1016/0967-0661(95)00126-F. Online. Available: http://dx.doi.org/10.1016/0967-0661(95)00126-F

A. Anzaldo-Meneses, and F. Monroy-Pérez, “Foucault pendulum and sub-Riemannian geometry”, Journal of Mathematical Physics, vol. 51, no. 8, article 082703, Aug. 2010. doi:10.1063/1.3478552. Online. Available: http://dx.doi.org/10.1063/1.3478552

V. I. Arnol'd, Mathematical Methods of Classical Mechanics. New York: Springer-Verlag, 1989. doi:10.1007/978-1-4757-2063-1. Online. Available: http://dx.doi.org/10.1007/978-1-4757-2063-1

G. Barenboim, and J. A. Oteo, “One pendulum to run them all”, European Journal of Physics, vol. 34, no. 4, pp. 1049-1065, May 2013. doi:10.1088/0143-0807/34/4/1049. Online. Available: http://dx.doi.org/10.1088/0143-0807/34/4/1049

I. G. Carmona, and J. Collado, “Control of a two wired hammerhead tower crane”, Nonlinear Dynamics, vol. 84, no. 4, pp. 2137-2148, June 2016. doi:10.1007/s11071-016-2634-3. Online. Available: http://dx.doi.org/10.1007/s11071-016-2634-3

A. S. Chessin, “On Foucault's Pendulum”, American Journal of Mathematics, vol. 17, no. 1, pp. 81-88, Jan. 1895. doi:10.2307/2369710. Online. Available: http://dx.doi.org/10.2307/2369710

D. Condurache, and V. Martinusi, “Foucault Pendulum-like problems: a tensorial approach”, International Journal of Non-Linear Mechanics, vol. 43, no. 8, pp. 743-760, October 2008. doi:10.1016/j.ijnonlinmec.2008.03.009. Online. Available: http://dx.doi.org/10.1016/j.ijnonlinmec.2008.03.009

U. Das, B. Talukdar, and J. Shamanna, “Indirect Analytic Representation of Foucault's Pendulum”, Czechoslovak Journal of Physics, vol. 52, no. 12, pp. 1321-1327, Dec. 2002. doi:10.1023/A:1021819627736. Online. Available: http://dx.doi.org/10.1023/A:1021819627736

R. M. Ghigliazza, and P. Holmes, “On the dynamics of cranes, or spherical pendula with moving supports”, International Journal of Non-Linear Mechanics, vol. 37, no. 7, pp. 1211-1221, Oct. 2002. doi:10.1016/S0020-7462(01)00141-X. Online. Available: http://dx.doi.org/10.1016/S0020-7462(01)00141-X

A. V. Gusev, V. N. Rudenko, and M. P. Vinogradov, “Spherical Pendulum in Gravitational Experiments”, Progress of Theoretical Physics, vol. 98, no. 3, pp. 587-599, Sep. 1997. doi:10.1143/PTP.98.587. Online. Available: http://dx.doi.org/10.1143/PTP.98.587

M. Gürgöze, “On the Formulation of Lagrange's Equations with Respect to Moving Coordinate Systems: Application to a Point Mass Vibrating on a Rotating Base”, International Journal of Mechanical Engineering Education, vol. 34, no. 3, pp. 263-272, July 2006. doi:10.7227/IJMEE.34.3.7. Online. Available: http://dx.doi.org/10.7227/IJMEE.34.3.7

E. Herrera, and S. Morett, “On the direction of Coriolis force and the angular momentum conservation”, Revista Brasileira de Ensino de Física, vol. 38, no. 3, article e3304, June 2016. doi:10.1590/1806-9126-RBEF-2016-0027. Online. Available: http://dx.doi.org/10.1590/1806-9126-RBEF-2016-0027

M. de Icaza-Herrera, and V. M. Castaño, “Generalized Lagrangian of the parametric Foucault pendulum with dissipative forces”, Acta Mechanica, vol. 218, no. 1-2, pp. 45-64, April 2011. doi:10.1007/s00707-010-0392-8. Online. Available: http://dx.doi.org/10.1007/s00707-010-0392-8

F. Ju, Y. S. Choo, and F. S. Cui, “Dynamic response of tower crane induced by the pendulum motion of the payload”, International Journal of Solids and Structures, vol. 43, no. 2, pp. 376-389, Jan. 2006. doi:10.1016/j.ijsolstr.2005.03.078. Online. Available: http://dx.doi.org/10.1016/j.ijsolstr.2005.03.078

S. E. Khaikin, Fizicheskie osnovy mekhaniki [Physical Foundations of Mechanics] (izd. 2-e, ispr. i dop. [2nd ed.]). Moskva [Moscow]: Nauka, 1971. (in Russian)

W. S. Kimball, “The Foucault Pendulum Star Path and the n-Leaved Rose”, American Journal of Physics, vol. 13, no. 5, pp. 271-277, Oct. 1945. doi:10.1119/1.1990726. Online. Available: http://dx.doi.org/10.1119/1.1990726

A. A. Kostikov, A. V. Perig, D. Yu. Mikhieienko, and R. R. Lozun, “Numerical JModelica.org-based approach to a simulation of Coriolis effects on guided boom-driven payload swaying during non-uniform rotary crane boom slewing”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 39, no. 3, pp. 737-756, March 2017. doi:10.1007/s40430-016-0554-2. Online. Available: http://dx.doi.org/10.1007/s40430-016-0554-2

A. A. Kostikov, A. V. Perig, and R. R. Lozun, “Simulation-assisted teaching of graduate students in transport: A case study of the application of acausal freeware JModelica.org to solution of Sakawa’s open-loop optimal control problem for payload motion during crane boom rotation”, International Journal of Mechanical Engineering Education, vol. 45, no. 1, pp. 3-27, Jan. 2017. doi:10.1177/0306419016669033. Online. Available: http://dx.doi.org/10.1177/0306419016669033

L. D. Landau, and E. M. Lifshitz, Mechanics (Vol. 1 of Course of Theoretical Physics). Oxford: Butterworth-Heinemann, 1976.

J. A. Linnett, “Methods of Using a Vibratory System to Measure Small Rates of Turn”, Journal of Mechanical Engineering Science, vol. 11, no. 5, pp. 526-533, Oct. 1969. doi:10.1243/JMES_JOUR_1969_011_064_02. Online. Available: http://dx.doi.org/10.1243/JMES_JOUR_1969_011_064_02

G. N. Mill, V. S. da Costa, and A. de M. Paiva, “Projeto de uma mesa giratória para simulação de escoamentos geofísicos (Design of a rotating table for simulating geophysical flows)”, Revista Brasileira de Ensino de Física, vol. 37, no. 4, article e4302, Out./Dez. 2015. doi:10.1590/S1806-11173731930. Online. Available: http://dx.doi.org/10.1590/S1806-11173731930

A. B. Modelon, “JModelica.org User Guide: Version 1.17”, 2015. Online. Available: http://www.jmodelica.org/api-docs/usersguide/JModelicaUsersGuide-1.17.0.pdf

H. Netuzhylov, and A. Zilian, “Meshfree collocation method for implicit time integration of ODEs”, International Journal of Computational Methods, vol. 08, no. 01, pp. 119-137, March 2011. doi: 10.1142/S0219876211002514. Online. Available: http://dx.doi.org/10.1142/S0219876211002514

W. J. Noble, “A direct treatment of the Foucault pendulum”, American Journal of Physics, vol. 20, no. 6, pp. 334-336, 1952. doi:10.1119/1.1933230. Online. Available: http://dx.doi.org/10.1119/1.1933230

M. Pardy, “Bound Motion of Bodies and Paticles in the Rotating Systems”, International Journal of Theoretical Physics, vol. 46, no. 4, pp. 848-859, Apr. 2007. doi:10.1007/s10773-006-9244-7. Online. Available: http://dx.doi.org/10.1007/s10773-006-9244-7

A. V. Perig, A. N. Stadnik, and A. I. Deriglazov, “Spherical pendulum small oscillations for slewing crane motion”, The Scientific World Journal, vol. 2014, Article ID 451804, 10 pp., Jan. 2014. doi:10.1155/2014/451804. Online. Available: http://dx.doi.org/10.1155/2014/451804

A. V. Perig, A. N. Stadnik, A. I. Deriglazov, and S. V. Podlesny, “3 DOF spherical pendulum oscillations with a uniform slewing pivot center and a small angle assumption”, Shock and Vibration, vol. 2014, Article ID 203709, 32 pp., Aug. 2014. doi:10.1155/2014/203709. Online. Available: http://dx.doi.org/10.1155/2014/203709

A. V. Perig, A. N. Stadnik, A. A. Kostikov, and S. V. Podlesny, “Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes”, Shock and Vibration, vol. 2017, Article ID 9605657, 21 pp., Feb. 2017. doi:10.1155/2017/9605657. Online. Available: http://dx.doi.org/10.1155/2017/9605657

A. Persson, “Is the Coriolis effect an ‘optical illusion’?”, Quarterly Journal of the Royal Meteorological Society, vol. 141, no. 690, pp. 1957-1967, July 2015 Part A, doi:10.1002/qj.2477. Online. Available: http://dx.doi.org/10.1002/qj.2477

N. Phillips, “What Makes the Foucault Pendulum Move among the Stars?”, Science & Education, vol. 13, no. 7-8, pp. 653-661, Nov. 2004. doi:10.1007/s11191-004-9471-3. Online. Available: http://dx.doi.org/10.1007/s11191-004-9471-3

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes. New York: Wiley, 1962.

J. L. Rosner, and S. A. Slezak, “Classical illustrations of CP violation in kaon decays”, American Journal of Physics, vol. 69, no. 1, pp. 44-49, 2001. doi:10.1119/1.1289212. Online. Available: http://dx.doi.org/10.1119/1.1289212

Y. Sakawa, Y. Shindo, and Y. Hashimoto, “Optimal control of a rotary crane”, Journal of Optimization Theory and Applications, vol. 35, no. 4, pp. 535-557, Dec. 1981. doi:10.1007/BF00934931. Online. Available: http://dx.doi.org/10.1007/BF00934931

E. O. Schulz-DuBois, “Foucault Pendulum Experiment by Kamerlingh Onnes and Degenerate Perturbation Theory”, American Journal of Physics, vol. 38, no. 2, pp. 173-188, 1970. doi:10.1119/1.1976270. Online. Available: http://dx.doi.org/10.1119/1.1976270

K. Terashima, Y. Shen, and K. Yano, “Modeling and optimal control of a rotary crane using the straight transfer transformation method”, Control Engineering Practice, vol. 15, no. 9, pp. 1179-1192, Sep. 2007. doi:10.1016/j.conengprac.2007.02.008. Online. Available: http://dx.doi.org/10.1016/j.conengprac.2007.02.008

M. S. Tiersten, and H. Soodak, “Dropped objects and other motions relative to the noninertial earth”, American Journal of Physics, vol. 68, no. 2, pp. 129-142, Jan. 2000. doi:10.1119/1.19385. Online. Available: http://dx.doi.org/10.1119/1.19385

N. Uchiyama, H. Ouyang, S. Sano, “Simple rotary crane dynamics modeling and open-loop control for residual load sway suppression by only horizontal boom motion”, Mechatronics, vol. 23, no. 8, pp. 1223-1236, Dec. 2013. doi:10.1016/j.mechatronics.2013.09.001. Online. Available: http://dx.doi.org/10.1016/j.mechatronics.2013.09.001

A. Wiin-Nielsen, “A note on inertial motion”, Atmósfera, vol. 17, no. 3, pp. 183-190, 2004. Online. Available: http://ref.scielo.org/bbmg78

V. F. Zhuravlev, and A. G. Petrov, “The Lagrange Top and the Foucault Pendulum in Observed Variables”, Doklady Physics, vol. 59, no. 1, pp. 35-39, 2014. doi:10.1134/S102833581401008X. Online. Available: http://dx.doi.org/10.1134/S102833581401008X

J. Piaget, Introduction à l'épistémologie génétique: La pensée mathématique [Introduction to genetic epistemology: Vol. 1: Mathematical thought]. Paris: Presses Universitaires de France, 1950/1973. (in French)

Y. Chevallard, La Transposition didactique: du savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage, 1985. (in French)

M. Bosch, and J. Gascón, “Twenty-Five Years of the Didactic Transposition”, ICMI Bulletin, no. 58, pp. 51-65, June 2006. Online. Available: http://www.mathunion.org/fileadmin/ICMI/files/Publications/ICMI_bulletin/58.pdf

F. Wozniak, M. Bosch, and M. Artaud, “The anthropological theory of the didactic”, Online Newsletter of the Association pour la Recherche en Didactiques de Mathematiques (ARDM), 2010. Online. Available: http://www.ardm.eu/contenu/yves-chevallard-english

W. Kang, and J. Kilpatrick, “Didactic transposition in mathematics textbooks”, For the Learning of Mathematics, vol. 12, no. 1, pp. 2-7, Feb. 1992. Online. Available: http://flm-journal.org/Articles/53840B1E86320031E69B7938060517.pdf

T.-O. Cujbă, “Reconstruction of Contents by Raported to the Idea of Didactic Transposition”, International Journal of Social and Educational Innovation (IJSEIro), vol. 2, no. 3, pp. 91-102, 2015. Online. Available: http://oaji.net/articles/2015/1508-1427635307.pdf and http://media1.wgz.ro/files/media1:58dd28a013345.pdf.upl/Volume_2_Issue_3_IJSEIro.PDF

A. Klisinska, “The fundamental theorem of calculus: a case study into the didactic transposition of proof”, dissertation of Ph.D. (Mathematics Education), Luleå tekniska universitet (Luleå University of Technology), Luleå, 2009. Online. Available: http://ltu.diva-portal.org/smash/get/diva2:990885/FULLTEXT01.pdf

A. Beitone, C. Dollo, E. Hemdane, and J.-R. Lambert, Les sciences économiques et sociales. Enseignement et apprentissages. Bruxelles: de Boeck, 2013. (in French)

P.-O. Larsson, and R. Braun, “Construction and Control of an Educational Lab Process - The Gantry Crane”, presented at the Swedish Control Meeting, Reglermöte, Luleå, Sweden, 4-5 June 2008 (2008/06/04). Online. Available: http://portal.research.lu.se/portal/files/6200728/8229123.pdf

E. Seabra, and J. Machado, “Teaching Kinematics and Dynamics of Multibody Mechanical System Using the Object Oriented Language Modelica”, International Journal of Online Engineering (iJOE), vol. 5, no. 2, pp. 33-38, Nov. 2009. doi:10.3991/ijoe.v5s2.1096. Online. Available: http://dx.doi.org/10.3991/ijoe.v5s2.1096

J. Åkesson, K.-E. Årzén, M. Gäfvert, T. Bergdahl, H. Tummescheit, “Modeling and optimization with Optimica and JModelica.org – Languages and tools for solving large-scale dynamic optimization problems”, Computers & Chemical Engineering, vol. 34, no. 11, pp. 1737-1749, Nov. 2010. doi:10.1016/j.compchemeng.2009.11.011. Online. Available: http://dx.doi.org/10.1016/j.compchemeng.2009.11.011

S. Zhao, Z. Shi, and S. Zhu, “A virtual laboratory architecture for engineering education”, 2011 IEEE 3rd International Conference on Communication Software and Networks, Xi'an, pp. 560-563, 2011. doi:10.1109/ICCSN.2011.6013895. Online. Available: http://dx.doi.org/10.1109/ICCSN.2011.6013895

J. YuXiang, Z. Xiaolong, L. JinPing, and R. LiYing, “Modeling and Simulation of the Virtualized Scenes Base on the Open Modelica”, Applied Informatics and Communication. ICAIC 2011. Communications in Computer and Information Science, vol. 226, pp. 103-110, 2011. doi:10.1007/978-3-642-23235-0_14. http://dx.doi.org/10.1007/978-3-642-23235-0_14

L. Jianfeng, L. Hongjun, and M. Yumin, “A Framework of Network Virtual Experiments for Control Courses”, International Journal of Education and Management Engineering, vol. 2, no. 9, pp. 49-55, Sep. 2012. doi:10.5815/ijeme.2012.09.08. Online. Available: http://dx.doi.org/10.5815/ijeme.2012.09.08

D. Zimmer, “A Planar Mechanical Library for Teaching Modelica”, Proceedings of the 9th International MODELICA Conference, 3-5 September 2012, Munich, Germany. Linköping Electronic Conference Proceedings, no. 76, Article 69, pp. 681-690, Nov. 2012 (2012-11-19). doi:10.3384/ecp12076681. Online. Available: http://dx.doi.org/10.3384/ecp12076681

C. Martin-Villalba, A. Urquia, and S. Dormido, “Development of virtual-labs for education in chemical process control using Modelica”, Computers & Chemical Engineering, vol. 39, pp. 170-178, Apr. 2012. doi:10.1016/j.compchemeng.2011.10.010. Online. Available: http://dx.doi.org/10.1016/j.compchemeng.2011.10.010

C. Martin-Villalba, A. Urquia, and S. Dormido, “Development of an industrial boiler virtual-lab for control education using Modelica”, Computer Applications in Engineering Education, vol. 21, no. 1, pp. 36-45, 2013. doi:10.1002/cae.20449. Online. Available: http://dx.doi.org/10.1002/cae.20449

D. Winkler, and B. Lie, “Hydro Power Systems: Scripting Modelica Models for Operational Studies in Education”, Simulation Notes Europe, vol. 23, no. 3-4, pp. 179-184, Dec. 2013, doi:10.11128/sne.23.tn.10214. Online. Available: http://dx.doi.org/10.11128/sne.23.tn.10214

P. Palensky, E. Widl, and A. Elsheikh, “Simulating Cyber-Physical Energy Systems: Challenges, Tools and Methods”, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 44, no. 3, pp. 318-326, March 2014. doi:10.1109/TSMCC.2013.2265739. Online. Available: http://dx.doi.org/10.1109/TSMCC.2013.2265739

Z. Yanshan, Y. F. Fah, J. Singh, L. Ting, and G. Lei, “A knowledge-based web platform for collaborative physical system modeling and simulation”, Computer Applications in Engineering Education, vol. 23, no. 1, pp. 23-35, 2015. doi:10.1002/cae.21572. Online. Available: http://dx.doi.org/10.1002/cae.21572

F. Magnusson, and J. Åkesson, “Dynamic Optimization in JModelica.org”, Processes, vol. 3, no. 2, pp. 471-496, June 2015. doi:10.3390/pr3020471. Online. Available: http://dx.doi.org/10.3390/pr3020471

M. Wetter, M. Bonvini, and T. S. Nouidui, “Equation-based languages – A new paradigm for building energy modeling, simulation and optimization”, Energy and Buildings, vol. 117, pp. 290-300, Apr. 2016. doi:10.1016/j.enbuild.2015.10.017. Online. Available: http://dx.doi.org/10.1016/j.enbuild.2015.10.017

Allegoric Educational Crossroad for a Problems of Multi-Criteria Choice
Published
2017-12-30
Section
ICT and learning tools in the higher education establishments